scholarly journals Generalized tanh method with symbolic computation and generalized shallow water wave equation

1997 ◽  
Vol 33 (4) ◽  
pp. 115-118 ◽  
Author(s):  
Yi-Tian Gao ◽  
Bo Tian
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Shallow Water Wave ◽  
Tanh Method

Generalized tanh Method and Four Families of Soliton-Like Solutions for a Generalized Shallow Water Wave Equation

1996 ◽  
Vol 51 (3) ◽  
pp. 171-174 ◽  
Author(s):  
Bo Tian ◽  
Yi-Tian Gao
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Shallow Water Wave ◽  
Tanh Method

We report that a generalized tanh method with symbolic computation leads to 4 families of soliton-like solutions for the Jimbo-Miwa's (3 + 1)-dimensional generalized shallow water wave equation.

scholarly journals Lump solutions to the (2+1)-dimensional shallow water wave equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1765-1769 ◽  
Author(s):  
Hong-Cai Ma ◽  
Ke Ni ◽  
Aiping Deng
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Symbolic Computation ◽  
Linear Form ◽  
Water Wave ◽  
The Other ◽  
Translation Invariance ◽  
Lump Solutions ◽  
Shallow Water Wave ◽  
Free Parameters

Through symbolic computation with MAPLE, a class of lump solutions to the (2+1)-D shallow water wave equation is presented, making use of its Hirota bi-linear form. The resulting lump solutions contain six free parameters, two of which are due to the translation invariance of the (2+1)-D shallow water wave equation and the other four of which satisfy a non-zero determinant condition guaranteeing analyticity and rational localization of the solutions.

scholarly journals Exact Solutions and Conserved Vectors of the Two-Dimensional Generalized Shallow Water Wave Equation

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1439
Author(s):  
Chaudry Masood Khalique ◽  
Karabo Plaatjie
Keyword(s):  
Differential Equation ◽  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Elliptic Integral ◽  
Momentum Conservation ◽  
Two Dimensional ◽  
Order Ordinary Differential Equation ◽  
Closed Form Solutions ◽  
Shallow Water Wave

In this article, we investigate a two-dimensional generalized shallow water wave equation. Lie symmetries of the equation are computed first and then used to perform symmetry reductions. By utilizing the three translation symmetries of the equation, a fourth-order ordinary differential equation is obtained and solved in terms of an incomplete elliptic integral. Moreover, with the aid of Kudryashov’s approach, more closed-form solutions are constructed. In addition, energy and linear momentum conservation laws for the underlying equation are computed by engaging the multiplier approach as well as Noether’s theorem.

scholarly journals On a shallow water wave equation

Nonlinearity ◽  
1994 ◽  
Vol 7 (3) ◽  
pp. 975-1000 ◽  
Author(s):  
P A Clarkson ◽  
E L Mansfield
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Shallow Water Wave

Fission and fusion interaction phenomena of mixed lump kink solutions for a generalized (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

2018 ◽  
Vol 32 (15) ◽  
pp. 1850161 ◽  
Author(s):  
Yaqing Liu ◽  
Xiaoyong Wen
Keyword(s):  
Shallow Water ◽  
Symbolic Computation ◽  
Water Wave ◽  
Hirota’S Bilinear Method ◽  
Bilinear Method ◽  
Lump Solutions ◽  
Shallow Water Wave ◽  
Petviashvili Equation ◽  
Kink Soliton ◽  
Interaction Phenomena

In this paper, a generalized (3[Formula: see text]+[Formula: see text]1)-dimensional B-type Kadomtsev–Petviashvili (gBKP) equation is investigated by using the Hirota’s bilinear method. With the aid of symbolic computation, some new lump, mixed lump kink and periodic lump solutions are derived. Based on the derived solutions, some novel interaction phenomena like the fission and fusion interactions between one lump soliton and one kink soliton, the fission and fusion interactions between one lump soliton and a pair of kink solitons and the interactions between two periodic lump solitons are discussed graphically. Results might be helpful for understanding the propagation of the shallow water wave.

Sign in / Sign up

Export Citation Format

Share Document