In this paper,we delve into a generalized higher order Camassa-Holm type equation,(or,an ghmCH equation for short).We establish local well-posedness for this equation under the condition that the initial data uo belon...
Project supported by the National Natural Science Foundation of China (Grant Nos.12275144,12235007,and 11975131);K.C.Wong Magna Fund in Ningbo University。
Integrable systems play a crucial role in physics and mathematics.In particular,the traditional(1+1)-dimensional and(2+1)-dimensional integrable systems have received significant attention due to the rarity of integra...
Supported by National Natural Science Foundation of China under Grant Nos.11771186 and 11671177
We present an integrable sl(2)-matrix Camassa-Holm(CH)equation.The integrability means that the equation possesses zero-curvature representation and infinitely many conservation laws.This equation includes two undeter...
We investigate the orbital stability of the peakons for a generalized Camassa-Holm equation (gCH). Using variable transformation, a planar dynamical system is obtained from the gCH equation. It is shown that the plana...
Supported by the Global Change Research Program of China under Grant No 2015CB953904;the National Natural Science Foundation of China under Grant No 11435005;the Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No ZF1213;the K.C.Wong Magna Fund at Ningbo University;the UTRGV President's Endowed Professorship;the Seed Grant of the UTRGV College of Science
We study the Alice-Bob peakon system generated from an integrable peakon system using the strategy of the so- called Alice-Bob non-local KdV approach [Scientific Reports 7 (2017) 869]. Nonlocal integrable peakon equ...
This paper is contributed to study two new integrable four-component systems reduced from a multi-component generation of Camassa-Holm equation. Some double peakon solutions of both systems are described in an explici...
Supported by the National Natural Science Foundation of China under Grant No.11261037;the Natural Science Foundation of Inner Mongolia Autonomous Region under Grant No.2014MS0111;the Caoyuan Yingcai Program of Inner Mongolia Autonomous Region under Grant No.CYYC2011050;the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region under Grant No.NJYT14A04
We study the multi-peakon solutions for two new coupled Camassa–Holm equations, which include twocomponent and three-component Camassa–Holm equations. These multi-peakon solutions are shown in weak sense. In particu...
In this paper, the modified extended tanh method is used to construct more general exact solutions of a (2+1)-dimensional nonlinear SchrSdinger equation. With the aid of Maple and Matlab software, we obtain exact e...
This research was supported by the National Natural Science Foundation of China 11271357,11271195 and 41504078;by the CSC,the Foundation for Innovative Research Groups of the NNSFC 11321061 and the ITER-China Program 2014GB124005。
In this paper,we study the Camassa-Holm equation and the Degasperis-Procesi equation.The two equations are in the family of integrable peakon equations,and both have very rich geometric properties.Based on these geome...
Supported by National Natural Science Foundation of China under Grant Nos.11361017,11161013;Natural Science Foundation of Guangxi under Grant Nos.2012GXNSFAA053003,2013GXNSFAA019010;Program for Innovative Research Team of Guilin University of Electronic Technology
In this paper, we study peakon, cuspon, smooth soliton and periodic cusp wave of the generalized Schr6dinger-Boussinesq equations. Based on the method of dynamical systems, the generalized Schr6dinger-Boussinesq equat...