Results 111 to 120 of about 2,203 (128)

The Dynamics of Lump, Lumpoff and Rogue Wave Solutions of (2+1)-Dimensional Hirota-Satsuma-Ito Equations

, 2020
The Hirota-Satsuma-Ito equation in (2+1)-dimensions is studied and a new general representation of lump solutions is derived. If the lump soliton is generated by an exponentially localised line soliton, we obtain a lumpoff solution. On the other hand, if
Ling-Di Zhang
semanticscholar   +1 more source

Efficient and Accurate Legendre Spectral Element Methods for One-Dimensional Higher Order Problems

, 2021
Efficient and accurate Legendre spectral element methods for solving onedimensional higher order differential equations with high oscillatory or steep gradient solutions are proposed.
Yang Zhang
semanticscholar   +1 more source

Abundant Mixed Lump-Soliton Solutions to the BKP Equation

East Asian Journal on Applied Mathematics, 2018
Applying Maple symbolic computations, we derive eight sets of mixed lumpsoliton solutions to the (2 + 1)-dimensional BKP equation. The solutions are analytic and allow the separation of lumps and line solitons.
Jin-Yun Yang
semanticscholar   +1 more source

Novel Interaction Phenomena of Localised Waves in the (2 + 1)-Dimensional HSI Equation

, 2020
Localised interaction solutions of the (2+1)-dimensional generalised HirotaSatsuma-Ito equation are studied. Using the Hirota bilinear form and Maple symbolic computations, we generate three classes of lump solutions.
Hongcai Ma
semanticscholar   +1 more source

Conservative and Dissipative Local Discontinuous Galerkin Methods for Korteweg-de Vries Type Equations

Communications in Computational Physics, 2019
In this paper, we develop the Hamiltonian conservative and L2 conservative local discontinuous Galerkin (LDG) schemes for the Korteweg-de Vries (KdV) type equations with the minimal stencil. For the time discretization, we adopt the semiimplicit spectral
Qian Zhang, Yinhua Xia
semanticscholar   +1 more source

Lump Solutions of the Modified Kadomtsev-Petviashvili-I Equation

, 2020
The modified Kadomtsev-Petviashvili-I equation is studied by the Hirota bilinear method. Certain lump solutions of this equation are found via the ansatz technique.
X. Yong, Yuning Chen, Yehui Huang, W. Ma
semanticscholar   +1 more source

Dynamics of Solitary Waves and Periodic Waves in a (3 + 1)-Dimensional Nonlinear Evolution Equation

East Asian Journal on Applied Mathematics, 2018
The Hirota bilinear method is applied to a generalised (3 + 1)-dimensional nonlinear evolution equation. Using the Riemann theta function, we construct periodic wave solutions of the Eq. (1.1) and discuss their properties.
Xiu-Bin Wang
semanticscholar   +1 more source

On Invariant-Preserving Finite Difference Schemes for the Camassa-Holm Equation and the Two-Component Camassa-Holm System

, 2016
The purpose of this paper is to develop and test novel invariant-preserving finite difference schemes for both the Camassa-Holm (CH) equation and one of its 2-component generalizations (2CH).
Hailiang Liu, Terrance Pendleton
semanticscholar   +1 more source

Local Discontinuous Galerkin Methods for the Degasperis-Procesi Equation

, 2011
In this paper, we develop, analyze and test local discontinuous Galerkin (LDG) methods for solving the Degasperis-Procesi equation which contains nonlinear high order derivatives, and possibly discontinuous or sharp transition solutions.
Yan Xu, Chi-Wang Shu
semanticscholar   +1 more source

Lump and Rogue Wave Solutions of a Reduced (3 + 1)-Dimensional Shallow Water Equation

East Asian Journal on Applied Mathematics, 2018
Considering a reduced (3 + 1)-dimensional shallow water equation, we use Hirota formulation and symbolic calculation to derive positive lump solitons rationally localised in all directions of the (x , y)-plane.
Jia Dong
semanticscholar   +1 more source