Exact solutions of the (3+1)-dimensional generalized Boiti–Leon–Manna–Pempinelli equation

Author(s):  
Ai-Juan Zhou ◽  
Ya-Ru Guo

In this paper, we study exact solutions of the (3[Formula: see text]+[Formula: see text]1)-dimensional Boiti–Leon–Manna–Pempinelli equation. We employ the Hirota bilinear method to obtain the multi-solitary wave solutions, soliton resonant solutions, periodic solutions and interactional solutions and periodic resonant solutions. The corresponding asymptotic features and images are also clearly given.

2021 ◽  
Vol 6 (10) ◽  
pp. 11046-11075
Author(s):  
Wen-Xin Zhang ◽  
◽  
Yaqing Liu

<abstract><p>In this paper, the reverse space cmKdV equation, the reverse time cmKdV equation and the reverse space-time cmKdV equation are constructed and each of three types diverse soliton solutions is derived based on the Hirota bilinear method. The Lax integrability of three types of nonlocal equations is studied from local equation by using variable transformations. Based on exact solution formulae of one- and two-soliton solutions of three types of nonlocal cmKdV equation, some figures are used to describe the soliton solutions. According to the dynamical behaviors, it can be found that these solutions possess novel properties which are different from the ones of classical cmKdV equation.</p></abstract>


2021 ◽  
pp. 2150391
Author(s):  
Ghazala Akram ◽  
Naila Sajid

In this article, three mathematical techniques have been operationalized to discover novel solitary wave solutions of (2+1)-dimensional Maccari system, which also known as soliton equation. This model equation is usually of applicative relevance in hydrodynamics, nonlinear optics and plasma physics. The [Formula: see text] function, the hyperbolic function and the [Formula: see text]-expansion techniques are used to obtain the novel exact solutions of the (2+1)-dimensional Maccari system (arising in nonlinear optics and in plasma physics). Many novel solutions such as periodic wave solutions by [Formula: see text] function method, singular, combined-singular and periodic solutions by hyperbolic function method, hyperbolic, rational and trigonometric solutions by [Formula: see text]-expansion method are obtained. The exact solutions are shown through 3D graphics which present the movement of the obtained solutions.


2020 ◽  
Vol 34 (07) ◽  
pp. 2050053
Author(s):  
Min Gao ◽  
Hai-Qiang Zhang

In this paper, we investigate a [Formula: see text]-dimensional B-type Kadomtsev-Petviashvili (BKP) equation, which is a generalization of the [Formula: see text]-dimensional equation. Based on the Hirota bilinear method and the limit technique of long wave, we systematically construct a family of exact solutions of BKP equation including the [Formula: see text]-solitary wave solution, lump solution as well as interaction solution between lump waves and solitary waves.


2015 ◽  
Vol 70 (9) ◽  
pp. 775-779 ◽  
Author(s):  
Elsayed M.E. Zayed ◽  
Abdul-Ghani Al-Nowehy

AbstractIn this article, the multiple exp-function method and the linear superposition principle are employed for constructing the exact solutions and the solitary wave solutions for the (2+1)-dimensional Calogero–Bogoyavlenskii–Schiff (CBS) equation. With help of Maple and by using the multiple exp-method, we can get exact explicit one-wave, two-wave, and three-wave solutions, which include one-soliton-, two-soliton-, and three-soliton-type solutions. Furthermore, we apply the linear superposition principle to find n-wave solutions of the CBS equation. Two cases with specific values of the involved parameters are plotted for each two-wave and three-wave solutions.


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongan Xie ◽  
Shengqiang Tang

We study a class of high dispersive cubic-quintic nonlinear Schrödinger equations, which describes the propagation of femtosecond light pulses in a medium that exhibits a parabolic nonlinearity law. Applying bifurcation theory of dynamical systems and the Fan sub-equations method, more types of exact solutions, particularly solitary wave solutions, are obtained for the first time.


Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2017
Author(s):  
Sadullah Bulut ◽  
Mesut Karabacak ◽  
Hijaz Ahmad ◽  
Sameh Askar

In this study, first, fractional derivative definitions in the literature are examined and their disadvantages are explained in detail. Then, it seems appropriate to apply the (G′G)-expansion method under Atangana’s definition of β-conformable fractional derivative to obtain the exact solutions of the space–time fractional differential equations, which have attracted the attention of many researchers recently. The method is applied to different versions of (n+1)-dimensional Kadomtsev–Petviashvili equations and new exact solutions of these equations depending on the β parameter are acquired. If the parameter values in the new solutions obtained are selected appropriately, 2D and 3D graphs are plotted. Thus, the decay and symmetry properties of solitary wave solutions in a nonlocal shallow water wave model are investigated. It is also shown that all such solitary wave solutions are symmetrical on both sides of the apex. In addition, a close relationship is established between symmetric and propagated wave solutions.


2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Sachin Kumar ◽  
Ilyas Khan ◽  
Setu Rani ◽  
Behzad Ghanbari

In soliton theory, the dynamics of solitary wave solutions may play a crucial role in the fields of mathematical physics, plasma physics, biology, fluid dynamics, nonlinear optics, condensed matter physics, and many others. The main concern of this present article is to obtain symmetry reductions and some new explicit exact solutions of the (2 + 1)-dimensional Sharma–Tasso–Olver (STO) equation by using the Lie symmetry analysis method. The infinitesimals for the STO equation were achieved under the invariance criteria of Lie groups. Then, the two stages of symmetry reductions of the governing equation are obtained with the help of an optimal system. Meanwhile, this Lie symmetry method will reduce the STO equation into new partial differential equations (PDEs) which contain a lesser number of independent variables. Based on numerical simulation, the dynamical characteristics of the solitary wave solutions illustrate multiple-front wave profiles, solitary wave solutions, kink wave solitons, oscillating periodic solitons, and annihilation of parabolic wave structures via 3D plots.


2017 ◽  
Vol 21 (4) ◽  
pp. 1783-1788 ◽  
Author(s):  
Ying Jiang ◽  
Da-Quan Xian ◽  
Zheng-De Dai

In this work, we study the (2+1)-D Broer-Kaup equation. The composite periodic breather wave, the exact composite kink breather wave and the solitary wave solutions are obtained by using the coupled degradation technique and the consistent Riccati expansion method. These results may help us to investigate some complex dynamical behaviors and the interaction between composite non-linear waves in high dimensional models


2013 ◽  
Vol 340 ◽  
pp. 755-759
Author(s):  
Song Hua Ma

With the help of the symbolic computation system Maple and the (G'/G)-expansion approach and a special variable separation approach, a series of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave (MDWW) system is derived. Based on the derived solitary wave solution, some novel domino solutions and chaotic patterns are investigated.


2004 ◽  
Vol 59 (1-2) ◽  
pp. 29-34 ◽  
Author(s):  
Zhenya Yan

In this paper, new doubly-periodic solutions in terms of Weierstrass elliptic functions are investigated for the coupled nonlinear Schr¨odinger equation and systems of two coupled real scalar fields. Solitary wave solutions are also given as simple limits of doubly periodic solutions. - PACS: 03.40.Kf; 02.30Ik


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