Results 281 to 290 of about 7,942,123 (324)

Lump solutions of the BKP equation

Physics Letters A, 1990
The BKP equation (Date, Jimbo, Kashiwara and Miwa 1981, Jimbo and Miwa 1983) $${({{\rm{u}}_{\rm{t}}} + 15{\rm{u}}{{\rm{u}}_{{\rm{3x}}}} + 15{\rm{u}}_{\rm{x}}^{\rm{3}} - 15{{\rm{u}}_{\rm{x}}}{{\rm{u}}_{\rm{y}}} + {{\rm{u}}_{{\rm{5x}}}})_{\rm{x}}} - 5{{\rm{u}}_{{\rm{3x,y}}}} - 5{{\rm{u}}_{{\rm{yy}}}} - 0,$$ (1) is a 2+1 dimensional generalisation ...
C.R Gilson, J.J.C Nimmo
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Lump solutions of a nonlinear PDE containing a third-order derivative of time

Applied Mathematics Letters, 2021
A nonlinear partial differential equation combining with a third-order derivative of the time variable D x D t 3 is studied. By adding a new fourth-order derivative term, its lump solutions are explicitly constructed by the Hirota bilinear method and ...
Liyuan Ding, W. Ma, Qingxian Chen, Yehui Huang   +3 more
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Collisions between lump and soliton solutions

Applied Mathematics Letters, 2019
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Lump solutions of the 2D Toda equation

Mathematical Methods in the Applied Sciences, 2020
In this research, the lump solution, which is rationally localized and decays along the directions of space variables, of a 2D Toda equation is studied. The effective method of constructing the lump solutions of this 2D Toda equation is derived, and the constraint conditions that make the lump solutions analytical and positive are obtained as well ...
Yong‐Li Sun, Wen‐Xiu Ma, Jian‐Ping Yu   +2 more
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From 2Mth-order wronskian determinant solutions to Mth-order lump solutions for the (2+1)-Dimensional Kadomtsev–Petviashvili I equation

Wave motion, 2021
In this paper, the Mth-order lump solutions for the (2+1)-dimensional Kadomtsev–Petviashvili I equation are studied. Firstly, the Nth-order wronskian determinant solutions of the Hirota bilinear form of the (2+1)-dimensional Kadomtsev–Petviashvili I ...
Yaning Tang, Jinli Ma, Bingchang Zhou, Jiale Zhou   +3 more
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Lump and Lump–Kink Soliton Solutions of an Extended Boiti–Leon–Manna–Pempinelli Equation

International Journal of Nonlinear Sciences and Numerical Simulation, 2020
Abstract In this paper, the extended Boiti–Leon–Manna–Pempinelli equation (eBLMP) is first proposed, and by Ma’s [1] method, a class of lump and lump–kink soliton solutions is explicitly generated by symbolic computations. The propagation orbit, velocity and extremum of the lump solutions on (x,y) plane are studied in detail. Interaction
Guo, Han-Dong, Xia, Tie-Cheng
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Exploring cone-shaped solitons, breather, and lump-forms solutions using the lie symmetry method and unified approach to a coupled breaking soliton model

Physica Scripta
In this research article, we investigate the coupled breaking soliton (cBS) model using two distinct analytical methods, namely, the Lie symmetry approach and the Unified method.
Sachin Kumar, S. K. Dhiman
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Some lump solutions for a generalized (3+1)-dimensional Kadomtsev-Petviashvili equation

Applied Mathematics and Computation, 2020
In this paper, a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation, which can be reduced to the classical equation, is investigated based on the Hirota bilinear method. The lump and lump strip solutions for this equation are obtained with the
Xue Guan, Wenjun Liu, Qin Zhou, A. Biswas   +3 more
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A Lump Solution in SFT

2013
A concrete example of lump solution in bosonic open string field theory is presented and discussed. It is shown that the solution satisfies the equation of motion and is not a pure gauge. The expression of its energy is written down explicitly. The value of the energy, calculated both numerically and analytically turns out to be in agreement with that ...
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Uniqueness of lump solution to the KP‐I equation

Proceedings of the London Mathematical Society
AbstractThe KP‐I equation has family of solutions which decay to zero at space infinity. One of these solutions is the classical lump solution, which is a traveling wave, and the KP‐I equation in this case reduces to the Boussinesq equation. In this paper we classify all the ‘lump‐type’ solutions of the Boussinesq equation.
Liu, Yong, Wei, Juncheng, Yang, Wen
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