scholarly journals N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2027-2035 ◽  
Author(s):  
Mustafa Inc ◽  
Kamyar Hosseini ◽  
Majid Samavat ◽  
Mohammad Mirzazadeh ◽  
Mostafa Eslami ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Present Article ◽  
Bilinear Form ◽  
Three Dimensions ◽  
Current Work ◽  
Petviashvili Equation ◽  
N Wave

The present article studies a B-type Kadomtsev-Petviashvili equation with certain applications in the fluids. Stating with the Hirota?s bilinear form and adopting reliable methodologies, a group of exact solutions such as the N-wave and other solutions to the B-type Kadomtsev-Petviashvili equation is formally derived. Some figures in two and three dimensions are given to illustrate the characteristics of the obtained solutions. The results of the current work actually help to complete the previous studies about the B-type Kadomtsev-Petviashvili equation.

Application of the exp(-φ)-expansion method to the Pochhammer-Chree equation

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3347-3354 ◽  
Author(s):  
Nematollah Kadkhoda ◽  
Michal Feckan ◽  
Yasser Khalili
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Present Article ◽  
Analytical Solutions ◽  
Nonlinear Differential Equations ◽  
Nonlinear Partial Differential Equations ◽  
Rational Functions ◽  
Expansion Method ◽  
Exponential Functions

In the present article, a direct approach, namely exp(-?)-expansion method, is used for obtaining analytical solutions of the Pochhammer-Chree equations which have a many of models. These solutions are expressed in exponential functions expressed by hyperbolic, trigonometric and rational functions with some parameters. Recently, many methods were attempted to find exact solutions of nonlinear partial differential equations, but it seems that the exp(-?)-expansion method appears to be efficient for finding exact solutions of many nonlinear differential equations.

A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.

Abundant Lump Solution and Interaction Phenomenon of (3+1)-Dimensional Generalized Kadomtsev–Petviashvili Equation

2019 ◽  
Vol 20 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Jianqing Lü ◽  
Sudao Bilige ◽  
Xiaoqing Gao
Keyword(s):  
Symbolic Computation ◽  
Bilinear Form ◽  
Lump Solution ◽  
Lump Solutions ◽  
Interaction Solution ◽  
Interaction Solutions ◽  
Petviashvili Equation ◽  
Contour Plots ◽  
Special Case ◽  
Interaction Phenomenon

AbstractIn this paper, with the help of symbolic computation system Mathematica, six kinds of lump solutions and two classes of interaction solutions are discussed to the (3+1)-dimensional generalized Kadomtsev–Petviashvili equation via using generalized bilinear form with a dependent variable transformation. Particularly, one special case are plotted as illustrative examples, and some contour plots with different determinant values are presented. Simultaneously, we studied the trajectory of the interaction solution.

Exact solutions with elastic interactions for the (2 $$+$$ 1)-dimensional extended Kadomtsev–Petviashvili equation

2020 ◽  
Vol 101 (4) ◽  
pp. 2413-2422
Author(s):  
Jutong Guo ◽  
Jingsong He ◽  
Maohua Li ◽  
Dumitru Mihalache
Keyword(s):  
Exact Solutions ◽  
Elastic Interactions ◽  
Petviashvili Equation

Asymptotic expansions for solitary gravity-capillary waves in two and three dimensions

2009 ◽  
Vol 465 (2109) ◽  
pp. 2725-2749 ◽  
Author(s):  
M. J. Ablowitz ◽  
T. S. Haut
Keyword(s):  
Surface Tension ◽  
Solitary Wave ◽  
Solitary Waves ◽  
Asymptotic Series ◽  
High Order ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Small Surface ◽  
Petviashvili Equation ◽  
Dimensional Series

High-order asymptotic series are obtained for two- and three-dimensional gravity-capillary solitary waves. In two dimensions, the first term in the asymptotic series is the well-known sech 2 solution of the Korteweg–de Vries equation; in three dimensions, the first term is the rational lump solution of the Kadomtsev–Petviashvili equation I. The two-dimensional series is used (with nine terms included) to investigate how small surface tension affects the height and energy of large-amplitude waves and waves close to the solitary version of Stokes’ extreme wave. In particular, for small surface tension, the solitary wave with the maximum energy is obtained. For large surface tension, the two-dimensional series is also used to study the energy of depression solitary waves. Energy considerations suggest that, for large enough surface tension, there are solitary waves that can get close to the fluid bottom. In three dimensions, analytic solutions for the high-order perturbation terms are computed numerically, and the resulting asymptotic series (to three terms) is used to obtain the speed versus maximum amplitude curve for solitary waves subject to sufficiently large surface tension. Finally, the above asymptotic method is applied to the Benney–Luke (BL) equation, and the resulting asymptotic series (to three terms) is verified to agree with the solitary-wave solution of the BL equation.

On converging shock waves

1987 ◽  
Vol 413 (1845) ◽  
pp. 297-311 ◽  
Keyword(s):  
Exact Solutions ◽  
Cross Sections ◽  
Three Dimensions ◽  
General Tendency ◽  
Approximate Theory ◽  
Regular Reflection ◽  
Converging Shock Waves ◽  
Shock Dynamics ◽  
Initial Shock ◽  
Polygonal Shape

An approximate theory of shock dynamics is used to study the behaviour of converging cylindrical shocks. For cylindrical shocks with regular polygonal-shaped cross sections, exact solutions are found, showing that an original polygonal shape repeats at successive intervals with successive contractions in scale. In this sense, these shapes are stable, and the successive Mach numbers increase according to exactly the same formula as for a circular cylindrical shock. The behaviour for initial shock shapes close to these and the general tendency of perturbed circular shapes to become polygonal, not necessarily regular, is explored numerically. Further analytical results are provided for rectangular shapes. Comments are made on the interpretation of regular reflection in this theory and on converging shocks in three dimensions.

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