Results 61 to 70 of about 1,267 (106)

Soliton equations: admitted solutions and invariances via B\"acklund transformations [PDF]

Open Communications in Nonlinear Mathematical Physics
A couple of applications of B\"acklund transformations in the study of nonlinear evolution equations is here given. Specifically, we are concerned about third order nonlinear evolution equations.
Sandra Carillo, Cornelia Schiebold
doaj   +1 more source

Global well-posedness for KdV in Sobolev Spaces of negative index [PDF]

, 2001
The initial value problem for the Korteweg-deVries equation on the line is shown to be globally well-posed for rough data.
Colliander, J., Keel, M., Staffilani, G., Takaoka, H., Tao, T.   +4 more
core   +1 more source

The exact solutions for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation

Results in Physics, 2021
In the paper, we study the Boiti-Leon-Manna-Pempinelli equation with (3 + 1) dimension. By using the modified hyperbolic tangent function method, we obtain more new exact solutions for the (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation, which ...
Xiaofang Duan, Junliang Lu
doaj  

Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System

, 2010
In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% \rho_{t}+k_{2}u\rho_{x}+(k_{1}+k_{2})\rho u_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\rho\rho_{x}=0. By the separation method,
Camassa, Deng, Escher, Goldreich, Guan, Guo, Ivanov, Jin, Lakin, Li, Liu, Makino, Manwai Yuen, Popowicz, Yuen, Yuen, Yuen, Yuen, Yuen, Zhou   +19 more
core   +1 more source

A novel integrability analysis of a generalized Riemann type hydrodynamic hierarchy

, 2018
The complete integrability of a generalized Riemann type hydrodynamic hierarchy is studied by means of a novel combination of symplectic and differential-algebraic tools.
A. Samoilenko, Y. Prykarpatskyy, D. Blackmore, A. Prykarpatski   +3 more
semanticscholar   +1 more source

Peaked solitary waves and shock waves of the Degasperis-Procesi-Kadomtsev-Petviashvili equation

Advances in Nonlinear Analysis
In this study, we establish the existence and nonexistence of smooth and peaked solitary wave solutions (or periodic) to the Degasperis-Procesi-Kadomtsev-Petviashvili (DP-KP) equation with a weak transverse effect.
Moon Byungsoo, Yang Chao
doaj   +1 more source

Sharp well-posedness for the cubic NLS and mKdV in $H^s({{\mathbb {R}}})$

Forum of Mathematics, Pi
We prove that the cubic nonlinear Schrödinger equation (both focusing and defocusing) is globally well-posed in $H^s({{\mathbb {R}}})$ for any regularity $s>-\frac 12$ .
Benjamin Harrop-Griffiths, Rowan Killip, Monica Vişan   +2 more
doaj   +1 more source

Theoretical analysis of a water wave model with a nonlocal viscous dispersive term using the diffusive approach

Advances in Nonlinear Analysis, 2017
In this paper, we study the following water wave model with a nonlocal viscous term:
Goubet Olivier, Manoubi Imen
doaj   +1 more source

The initial-value problem for a Gardner-type equation

Advanced Nonlinear Studies
Discussed here is a regularized version(0.1)ut+ux+uux+Au2ux−uxxt=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}-{u}_{\mathit{xxt}}=0,$$ of the classical Gardner equationut+ux+uux+Au2ux+uxxx=0, $${u}_{t}+{u}_{x}+u{u}_{x}+A{u}^{2}{u}_{x}+{u}_{\mathit{xxx ...
Bona Jerry, Chen Hongqiu, Guerrero Pamela, Haidau Cristina, Pantic Sanja   +4 more
doaj   +1 more source

On the existence of bound and ground states for some coupled nonlinear Schrödinger–Korteweg–de Vries equations

Advances in Nonlinear Analysis, 2017
We show the existence of positive bound and ground states for a system of coupled nonlinear Schrödinger–Korteweg–de Vries equations. More precisely, we prove that there exists a positive radially symmetric ground state if either the coupling coefficient ...
Colorado Eduardo
doaj   +1 more source