New exact periodic solitary-wave solutions for the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si9.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional generalized KP and BKP equations

Tang, Yaning; Zai, Weijian

doi:10.1016/j.camwa.2015.09.017

Cited by 15 publications

(2 citation statements)

References 31 publications

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“…16,17 Other searchers applied various methods as homoclinic breather limit (HBL) method, EHTA method, multiple exp-function method, the simplest equation method, Wronskian technique, and Bäcklund transformation. 2,3,[18][19][20] Yasar 21 used two stages of Lie symmetry reduction to reduce the (3 + 1)-dimensional BKP to some ODEs that had no quadrature and then tried to solve these equations using power series method and the simplest equation method with the aid of the prolongation theorem to investigate the Lie infinitesimals for Equation (1).…”

Section: Introductionmentioning

confidence: 99%

Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation

Saleh

Sadat

Kassem

2019

Math Methods in App Sciences

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We explored and specialized new Lie infinitesimals for the (3 + 1)-dimensional B-Kadomtsev-Petviashvii (BKP) using the commutation product, which results a system of nonlinear ODEs manually solved. Through two stages of Lie symmetry reduction, (3 + 1)-dimensional BKP equation is reduced to nonsolvable nonlinear ODEs using various combinations of optimal Lie vectors.Using the integration and Riccati equation methods, we investigate new analytical solutions for these ODEs. Back substituting to the original variables generates new solutions for BKP. Some selected solutions illustrated through three-dimensional plots. KEYWORDS(3 + 1)-dimensional B-Kadomtsev-Petviashvii (BKP), integrating factor, partial differential equations, Riccati equation, symmetry analysis MSC CLASSIFICATION

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Section: Introductionmentioning

confidence: 99%

Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation

Saleh

Sadat

Kassem

2019

Math Methods in App Sciences

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“…The study of the BKP equation has attracted a considerable size of research work. These equations were studied using the Hirota method, the multiple exp-function algorithm, the Pfaffian technique, Riemann theta functions, the extended homoclinic test approach, and Bäcklund transformation by many authors [17][18][19][20][21][22][23][24][25][26]. In this paper, based on the Wronskian method, the new exact solutions including rational solutions, soliton solutions, positon solutions, negaton solutions, and their interaction solutions of the (3+1)-dimensional generalized BKP equations are investigated.…”

Section: Introductionmentioning

confidence: 99%

New Exact Solutions for the (3+1)-Dimensional Generalized BKP Equation

2016

Discrete Dynamics in Nature and Society

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The Wronskian technique is used to investigate a (3+1)-dimensional generalized BKP equation. Based on Hirota’s bilinear form, new exact solutions including rational solutions, soliton solutions, positon solutions, negaton solutions, and their interaction solutions are formally derived. Moreover we analyze the strangely mechanical behavior of the Wronskian determinant solutions. The study of these solutions will enrich the variety of the dynamics of the nonlinear evolution equations.

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New singular wave solutions to the KdV‐Sawada‐Kotera‐Ramani equation by the modified simple equation method

Chen

2021

Math Methods in App Sciences

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The singular solutions and some special solutions of the KdV‐Sawada‐Kotera‐Ramani equation which have been analyzed in detail with solution functions supplemented by the relevant 3‐dimensional presentations of them. In the paper, very large number of possible concrete solutions are presented and discussed, based on the very various choices of possible values of the integration constants existing in the general solution function forms of the relevant class of problems being investigated. The contents of the main chapters have been classified and represented in a more concise and informative manner by pointing out the most important characteristics of the relevant solution sub‐results related by the actually chosen sub‐system of the general system of coupled ordinary differential equations and this process motivated this very detailed study. Finally, this paper obtains the unusually widespread collection of all these relatively laborsome solutions' set which can promote the application of the equation.

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New exact periodic solitary-wave solutions for the(3+1)-dimensional generalized KP and BKP equations

Cited by 15 publications

References 31 publications

Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation

Optimal solutions of a (3 + 1)‐dimensional B‐Kadomtsev‐Petviashvii equation

New Exact Solutions for the (3+1)-Dimensional Generalized BKP Equation

New singular wave solutions to the KdV‐Sawada‐Kotera‐Ramani equation by the modified simple equation method

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