Modulation theory and dispersive shock waves

Workshop theme

Whitham modulation theory has developed into a powerful mathematical tool to describe the intermediate and long-time behaviour of solutions to conservative or nearly conservative nonlinear dispersive equations. The theory achieved recognition with the successful description of dispersive shock waves (DSWs), identified nowadays in an abundant variety of physical applications.

The workshop will focus on modern research in nonlinear modulation theory and will include (but won’t be limited to) the following major themes:

(i) DSWs and related structures in integrable and non-integrable systems with particular emphasis on non-convex and multi-dimensional dispersive hydrodynamics

(ii) theoretical analysis of modulation systems

(iii) numerical realisation of DSWs

(iv) physical applications

Applications for this workshop are now closed

Fees

Registration Only

Registration Package: £208
Student Registration Package: £158

The Registration Package includes admission to all seminars, lunches and refreshments on the days that lectures take place (Monday - Friday), wine reception and formal dinner, but does not include other meals or accommodation.

Registration and Accommodation

Accommodation Package: £587

The Accommodation Package includes a registration fee, bed and breakfast accommodation at Churchill College from the evening of Sunday to breakfast on Saturday, together with lunches and refreshments during the days that lectures take place (Monday - Friday). The formal dinner is also included, but no other evening meals

Formal Dinner Only

Formal Dinner: £55

Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event. For all remaining participants who would like to attend, such as programme participants, the above charge will apply.

Accommodation

Accommodation in single study bedrooms with shared facilities and breakfast are provided at Churchill College.

Meals

Lunch

Lunch timings and location will be confirmed with timetable.

Evening Meal

Participants are free to make their own arrangements for dinner.

Formal Dinner

The Formal Dinner location and date is to be confirmed. Participants on the Accommodation Package or Registration Package, including organisers and speakers, are automatically included in this event.

The Institute kindly requests that any papers published as a result of this programme’s activities are credited as such. Please acknowledge the support of the Institute in your paper using the following text:

The author(s) would like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for support and hospitality during the programme Modulation theory and dispersive shock waves, where work on this paper was undertaken. This work was supported by EPSRC grant EP/R014604/1.

Timetable

Monday 11th July 2022
09:00 to 09:55	Registration	No Room Required
09:55 to 10:00	Ulrike Tillmann University of Oxford Welcome Talk	Room 1
10:00 to 11:00	Thomas Bridges University of Surrey Chair: Gennady El Whitham modulation theory and water waves	Room 1
11:00 to 11:30	Morning Coffee	No Room Required
11:30 to 12:00	Daniel Ratliff Northumbria University Chair: Gennady El Frequency Downshifting: A Dispersive Whitham Perspective	Room 1
12:00 to 14:00	Lunch	No Room Required
14:00 to 14:30	Wesley Perkins Lehigh University; Lyon College Chair: Thibault Congy Modulational Stability for Equations of Whitham Type	Room 1
14:30 to 15:00	Stanislav Opanasenko Loughborough University Chair: Thibault Congy Linearisable Abel equations and the Gurevich-Pitaevskii problem	Room 1
15:00 to 15:30	Benjamin Doyon King's College London Chair: Thibault Congy The hydrodynamics of soliton gases	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Nicolas Pavloff Université Paris-Saclay Chair: Thibault Congy Modulation theory in two-component Bose-Einstein condensates: the ferromagnetic paradigm	Room 1
16:30 to 17:00	Lev Ostrovsky University of Colorado Boulder Chair: Thibault Congy Modulated Waves in Electrodynamics and Optics. Historical Perspective	Room 1
17:00 to 18:00	Welcome Wine Reception at INI	No Room Required

Tuesday 12th July 2022
09:00 to 10:00	Gino Biondini University at Buffalo Chair: Catherine Sulem Whitham modulation theory for multidimensional nonlinear evolution equations and applications	Room 1
10:00 to 10:30	Morning Coffee	No Room Required
10:30 to 11:00	Xudan Luo Chinese Academy of Sciences Chair: Catherine Sulem Three-dimensional internal waves in the lower atmosphere	Room 1
11:00 to 11:30	Karima Khusnutdinova Loughborough University Chair: Catherine Sulem On surface and internal ring waves on currents: dispersive hydrodynamics in 3D	Room 1
11:30 to 12:00	Wooyoung Choi New Jersey Institute of Technology Chair: Catherine Sulem Modulation of short surface waves by long internal waves	Room 1
12:00 to 14:00	Lunch	No Room Required
14:00 to 14:30	Ted Johnson University College London Chair: Anna Vainchtein Dispersive shock waves in coastal flows	Room 1
14:30 to 15:00	Ricardo Barros Loughborough University Chair: Anna Vainchtein Large mode-2 internal solitary waves in three-layer flows	Room 1
15:00 to 15:30	Michel Benoit Electricté de France Chair: Anna Vainchtein Soliton fission and solitonic turbulence for shallow water waves: a numerical study with different models	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required

Wednesday 13th July 2022
09:00 to 10:00	Anatoly Kamchatnov Russian Academy of Sciences; Moscow Institute of Physics and Technology Chair: Karima Khusnutdinova Whitham theory for perturbed integrable equations and nonlinear dynamics of solitons	Room 1
10:00 to 10:30	Morning Coffee	No Room Required
10:30 to 11:00	Anna Vainchtein University of Pittsburgh Chair: Karima Khusnutdinova Transition fronts and their universality classes	Room 1
11:00 to 11:30	Rosa Vargas-magana University of Edinburgh Chair: Karima Khusnutdinova Modulation Instability of undular bores in Whitham-Boussinesq systems and revealing characteristics of Stokes wave trains and solitary waves associated with these systems.	Room 1
11:30 to 12:00	Sergey Gavrilyuk Aix Marseille Université Chair: Karima Khusnutdinova Generalized Rankine -- Hugoniot relations for shocks in dispersive media	Room 1
12:00 to 14:00	Lunch	No Room Required
14:00 to 17:00	Free Afternoon	No Room Required
19:30 to 22:00	Formal Dinner at Emmanual College	No Room Required

Thursday 14th July 2022
09:00 to 10:00	Yuji Kodama Ohio State University Chair: Mark Hoefer Dispersive shock wave of the KP equation	Room 1
10:00 to 10:30	Morning Coffee	No Room Required
10:30 to 11:00	Efim Pelinovsky None / Other; University of Nizhny Novgorod Chair: Mark Hoefer Non-integrable KdV-like models: solitons, breathers, compactons and rogue waves	Room 1
11:00 to 11:30	Ali Demirci Instanbul Technical University Chair: Mark Hoefer Reductions of (2+1) and (3+1) Dimensional Kadomtsev- Petviashvili Type Equations and Dispersive Shock Waves	Room 1
11:30 to 12:00	Christopher Chong Bowdoin College Chair: Mark Hoefer Dispersive Shock Waves in Lattices: A Dimension Reduction Approach	Room 1
12:00 to 14:00	Lunch	No Room Required
14:00 to 14:30	Henrik Kalisch Universitetet i Bergen Chair: Ted Johnson Wave Breaking in Undular Bores	Room 1
14:30 to 15:00	Victor Shrira Keele University Chair: Ted Johnson Weakly nonlinear shoaling of tsunami: the phenomenon of self-induced transparency	Room 1
15:00 to 15:30	Dionyssis Mantzavinos University of Kansas Chair: Ted Johnson Initial-boundary value problems for Boussinesq-type systems	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 16:30	Pavel Lushnikov University of New Mexico; Landau Institute for Theoretical Physics Chair: Ted Johnson Statistical properties and giant fluctuations for laser beam propagating in a turbulent medium	Room 1
16:30 to 17:00	Bruno Lombard Laboratoire de Mécanique et d’Acoustique Chair: Ted Johnson Dynamics of a regularized and bistable Ericksen bar using an extended Lagrangian approach	Room 1

Friday 15th July 2022
09:00 to 10:00	Sylvie Benzoni-Gavage Université Claude Bernard Lyon 1; Institut Henri Poincaré Chair: Sergey Gavrilyuk Modulation equations revisited	Room 1
10:00 to 10:30	Morning Coffee	No Room Required
10:30 to 11:00	Maxim Pavlov Lebedev Physical Institute Chair: Sergey Gavrilyuk Integrable systems of the intermediate long wave type in 2 + 1 dimensions	Room 1
11:00 to 11:30	Christian Klein Université de Bourgogne Chair: Sergey Gavrilyuk Numerical Study of DSWs in Korteweg-de Vries and nonlinear Schrödinger equations	Room 1
11:30 to 12:00	Patrick Sprenger University of Cambridge Chair: Sergey Gavrilyuk Dispersive shock waves and traveling wave solutions of fifth-order KdV equations	Room 1
12:00 to 14:00	Lunch	No Room Required
14:00 to 14:30	L. Miguel Rodrigues Université de Rennes 1 Chair: Sylvie Benzoni-Gavage About plane periodic waves of the nonlinear Schrödinger equations	Room 1
14:30 to 15:00	Emilian I Parau University of East Anglia Chair: Sylvie Benzoni-Gavage Stability of waves on fluid of infinite depth with constant vorticity	Room 1
15:00 to 15:30	Thibault Congy Northumbria University Chair: Sylvie Benzoni-Gavage Dispersive Riemann problem for the Benjamin-Bona-Mahony equation	Room 1
15:30 to 16:00	Afternoon Tea	No Room Required
16:00 to 17:00	Close	Room 1

Dispersive hydrodynamics: mathematics, simulation and experiments, with applications in nonlinear waves

Modulation theory and dispersive shock waves

Organisers

Thibault Congy Northumbria University
Gennady El Northumbria University
Sergey Gavrilyuk Aix Marseille Université
Mark Hoefer University of Colorado Boulder

Speakers

Ricardo Barros Loughborough University
Michel Benoit Electricté de France
Sylvie Benzoni-Gavage Université Claude Bernard Lyon 1; Institut Henri Poincaré
Gino Biondini University at Buffalo
Thomas Bridges University of Surrey
Wooyoung Choi New Jersey Institute of Technology
Christopher Chong Bowdoin College
Thibault Congy Northumbria University
Ali Demirci Instanbul Technical University
Benjamin Doyon King's College London
Sergey Gavrilyuk Aix Marseille Université
Ted Johnson University College London
Henrik Kalisch Universitetet i Bergen
Anatoly Kamchatnov Russian Academy of Sciences; Moscow Institute of Physics and Technology
Karima Khusnutdinova Loughborough University
Christian Klein Université de Bourgogne
Yuji Kodama Ohio State University
Bruno Lombard Laboratoire de Mécanique et d’Acoustique
Xudan Luo Chinese Academy of Sciences
Pavel Lushnikov University of New Mexico; Landau Institute for Theoretical Physics
Dionyssis Mantzavinos University of Kansas
Stanislav Opanasenko Loughborough University
Lev Ostrovsky University of Colorado Boulder
Emilian I Parau University of East Anglia
Nicolas Pavloff Université Paris-Saclay
Maxim Pavlov Lebedev Physical Institute
Efim Pelinovsky None / Other; University of Nizhny Novgorod
Wesley Perkins Lehigh University; Lyon College
Daniel Ratliff Northumbria University
L. Miguel Rodrigues Université de Rennes 1
Victor Shrira Keele University
Patrick Sprenger University of Cambridge
Anna Vainchtein University of Pittsburgh
Rosa Vargas-magana University of Edinburgh

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Participants

Saleh Baqer University of Edinburgh
Ricardo Barros Loughborough University
Costanza Benassi Northumbria University
Michel Benoit Electricté de France
Sylvie Benzoni-Gavage Université Claude Bernard Lyon 1; Institut Henri Poincaré
Deniz Bilman University of Cincinnati
Gino Biondini University at Buffalo
Alexander Bivolcic University at Buffalo
Thibault Bonnemain Northumbria University
Thomas Bridges University of Surrey
Henry Carr Northumbria University
Alina Chertock North Carolina State University
Wooyoung Choi New Jersey Institute of Technology
Christopher Chong Bowdoin College
Thibault Congy Northumbria University
Ali Demirci Instanbul Technical University
Benjamin Doyon King's College London
Remy Dubertrand Northumbria University
Iryna Egorova B. Verkin Institute for Low Temperature Physics and Engineering
Gennady El Northumbria University
Gavin Esler University College London
Eugene Ferapontov Loughborough University
Sergey Gavrilyuk Aix Marseille Université
Andrey Gelash Novosibirsk State University; Skolkovo Institute of Science and Technology (Skoltech)
Manuela Girotti Saint Mary's University; Université de Montréal
Aikaterini Gkogkou University at Buffalo
Tamara Grava SISSA; University of Bristol
Mariana Haragus Université de Franche-Comté
James Herterich University College Dublin
Mark Hoefer University of Colorado Boulder
Vera Mikyoung Hur University of Illinois at Urbana-Champaign
Ted Johnson University College London
Divya Joseph Kayyunnapara None / Other
Henrik Kalisch Universitetet i Bergen
Anatoly Kamchatnov Russian Academy of Sciences; Moscow Institute of Physics and Technology
Panos Kevrekidis University of Massachusetts
Karima Khusnutdinova Loughborough University
Christian Klein Université de Bourgogne
Yuji Kodama Ohio State University
Bruno Lombard Laboratoire de Mécanique et d’Acoustique
Sara Lombardo Loughborough University
Xudan Luo Chinese Academy of Sciences
Pavel Lushnikov University of New Mexico; Landau Institute for Theoretical Physics
Dionyssis Mantzavinos University of Kansas
Yifeng Mao University of Colorado Boulder
Johanna Michor University of Vienna
Antonio Moro Northumbria University
Michael Nguyen University College London
Pascal Noble Université de Toulouse
Katie Oliveras Seattle University
Stanislav Opanasenko Loughborough University
Lev Ostrovsky University of Colorado Boulder
Emilian I Parau University of East Anglia
Maxim Pavlov Lebedev Physical Institute
Efim Pelinovsky None / Other; University of Nizhny Novgorod
Wesley Perkins Lehigh University; Lyon College
Barbara Prinari University at Buffalo
Stephane Randoux Université des Sciences et Technologies de Lille
Daniel Ratliff Northumbria University
Antoine Remond-Tiedrez University of Cambridge
Giacomo Roberti Northumbria University
L. Miguel Rodrigues Université de Rennes 1
Hayder Salman University of East Anglia
Michael Shearer North Carolina State University
Victor Shrira Keele University
Denis Silantyev University of Colorado Colorado Springs
Noel Smyth University of Edinburgh
Matteo Sommacal Northumbria University
Patrick Sprenger University of Cambridge
Catherine Sulem University of Toronto
Pierre Suret Université des Sciences et Technologies de Lille
Alexander Tovbis University of Central Florida
Olga Trichtchenko University of Western Ontario
Anna Vainchtein University of Pittsburgh
Rosa Vargas-magana University of Edinburgh
Stephen J. Watson University of Glasgow