## 3 Citations

### Finite gap conditions and small dispersion asymptotics for the classical periodic Benjamin–Ono equation

- MathematicsQuarterly of Applied Mathematics
- 2020

In this paper we characterize the Nazarov–Sklyanin hierarchy for the classical periodic Benjamin–Ono equation in two complementary degenerations: for the multiphase initial data (the periodic…

## References

SHOWING 1-10 OF 48 REFERENCES

### Model equations for long waves in nonlinear dispersive systems

- MathematicsPhilosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
- 1972

Several topics are studied concerning mathematical models for the unidirectional propagation of long waves in systems that manifest nonlinear and dispersive effects of a particular but common kind.…

### Integrable viscous conservation laws

- Mathematics
- 2013

We propose an extension of the Dubrovin–Zhang perturbative approach to the study of normal forms for non-Hamiltonian integrable scalar conservation laws. The explicit computation of the first few…

### Universality of the Break-up Profile for the KdV Equation in the Small Dispersion Limit Using the Riemann-Hilbert Approach

- Mathematics
- 2008

AbstractWe obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation
$$u_t+6uu_x+\epsilon^{2}u_{xxx}=0,\quad u(x,t=0,\epsilon)=u_0(x),$$for…

### Internal waves of permanent form in fluids of great depth

- Environmental ScienceJournal of Fluid Mechanics
- 1967

This paper presents a general theoretical treatment of a new class of long stationary waves with finite amplitude. As the property in common amongst physical systems capable of manifesting these…

### An extension of the steepest descent method for Riemann-Hilbert problems: the small dispersion limit of the Korteweg-de Vries (KdV) equation.

- MathematicsProceedings of the National Academy of Sciences of the United States of America
- 1998

This paper extends the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou in a critical new way to small dispersion KdV (Korteweg-de Vries) equation and derives the hyperelliptic asymptotic solution of S. Venakides that describes the oscillations.

### A Deformation of the Method of Characteristics and the Cauchy Problem for Hamiltonian PDEs in the Small Dispersion Limit

- Mathematics
- 2015

We introduce a deformation of the method of characteristics valid for Hamiltonian perturbations of a scalar conservation law in the small dispersion limit. Our method of analysis is based on the…

### On a functional equation related to the intermediate long wave equation

- Mathematics
- 2004

We resolve an open problem stated by Ablowitz et al (1982 J. Phys. A: Math. Gen. 15 781) concerning the integral operator appearing in the intermediate long wave equation. We explain how this is…

### The Small Dispersion Limit of the Korteweg-deVries Equation. I

- Mathematics
- 1982

In Part I the scattering transform method is used to study the weak limit of solutions to the initial value problem for the Korteweg-deVries (KdV) equation as the dispersion tends to zero. In that…

### Monodromy- and spectrum-preserving deformations I

- Mathematics
- 1980

A method for solving certain nonlinear ordinary and partial differential equations is developed. The central idea is to study monodromy preserving deformations of linear ordinary differential…