author={Sascha Vongehr},
  journal={Encyclopedia of Continuum Mechanics},
  • S. Vongehr
  • Published 2020
  • Encyclopedia of Continuum Mechanics
Algebraic structures on the flows of dispersionless modified KP equation
In this paper, we derive the non-isospectral flows of dispersionless modified Kadomtsev–Petviashvili (dmKP) hierarchies by applying quasiclassical limit in the associated Lax equations of the mKP
Finite gap conditions and small dispersion asymptotics for the classical periodic Benjamin–Ono equation
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
Solitons on the rarefactive wave background via the Darboux transformation
. Rarefactive waves and dispersive shock waves are generated from the step-like initial data in many nonlinear evolution equations including the classical example of the Korteweg-de Vries (KdV)
Riemann-Hilbert problems for a nonlocal reverse-spacetime Sasa-Satsuma hierarchy of a fifth-order equation and its soliton solutions
We aim to present and analyze a nonlinear nonlocal reverse-spacetime fifth-order scalar Sasa-Satsuma equation, based on a nonlocal 5 × 5 matrix AKNS spectral problem. Starting from a nonlocal matrix
Darboux transformation and solitonic solution to the coupled complex short pulse equation
SSP IMEX Runge-Kutta WENO Scheme for Generalized Rosenau-KdV-RLW Equation
In this article, we present a third-order weighted essentially non-oscillatory (WENO) method for generalized Rosenau-KdV-RLW equation. The third order finite difference WENO reconstruction and
Vector breather waves and higher-order rouge waves to the coupled higher-order nonlinear Schrödinger equations
The asymptotic expansion theory, which allows the solution of the equation to be iterated through the same spectral parameters, is introduced and the matrix exponential function and the Taylor multi-series expansion method are used to derive the vector breather wave solutions and the higher-order rouge wave solutions.
Microscopic conservation laws for the derivative Nonlinear Schrödinger equation
Compared with macroscopic conservation law for the solution of the derivative nonlinear Schrodingger equation (DNLS) with small mass in \cite{KlausS:DNLS}, we show the corresponding microscopic
Rational solutions of the defocusing non-local nonlinear Schrödinger equation: asymptotic analysis and soliton interactions
In this paper, we obtain the Nth-order rational solutions for the defocusing non-local nonlinear Schrödinger equation by the Darboux transformation and some limit technique. Then, via an improved
Numerical Analysis of Nonlinear Wave Propagation
Numerical analysis of nonlinear wave propagation Nonlinear partial differential equations (PDEs) arise in many areas of mathematical physics in order to model various physical phenomena. However, in