New exact solutions to extended (3 + 1)‐dimensional Jimbo‐Miwa equations by using bilinear forms

Abstract

In this work, we investigate extended (3 + 1)‐dimensional Jimbo‐Miwa equations by locating movable critical points with the aid of Painlevé analysis. We construct bilinear forms through using truncated Painlevé expansions along with the Bell polynomials approach. The proposed approach provides enough freedom to construct solutions that may be related to large variety of real physical phenomena, and in addition, this approach enriches the solution structure. Abundant exact solutions involving various arbitrary constants are furnished in uniform manner by using test function. The obtained solutions are entirely new and different from those reported in the literature.

Dynamics of higher-order bright and dark rogue waves in a new (2+1)-dimensional integrable Boussinesq model

“…This section is devoted for fabricating bilinear form of the Boussinesq equation (2) by making use of the Bell polynomials. A crisp description about the Bell polynomials can be studied with the help of reference [45] for a better understanding. Using the properties of Bell polynomials and considering the transformation…”

“…Based on the above, our motive in this work is to bring light on the rogue wave solutions and their dynamical characteristics for the considered equation (2), since, nowadays, theoretical analysis of such waves has become an integral segment of the field nonlinear sciences. The Hirota bilinear method [44][45][46][47] is found successful in investigating various nonlinear evolution equations to obtain rogue wave solutions and especially it was adopted for low order rogue wave solutions in these studies. Despite the high difficulty level in exploring multiple rogue waves, still, there are few works of literature on it.…”

Exact Solutions of an Extended Jimbo-Miwa Equation by Three Distinct Methods

“…So far, mathematicians and physicists have established several efective methods, such as F-expansion method, [19][20][21] the frst integral method, [22] dynamical system method, [23,24] improved Kudryashov method, [25][26][27] Hirota bilinear approach, [28][29][30][31] tan(Θ/2) expansion approach, [32] exp (− ϕ(ξ))-expansion method, [33] generalized exponential rational function method [34], and other methods [35]. Te (G ′ /G)-expansion method proposed by Wang et al [36] is one of the most efective direct methods to obtain travelling wave solutions of a large number of nonlinear evolution equations, such as the KdV equation, the mKdV equation, the variant Boussinesq equations, the Hirota-Satsuma equations, and so on.…”

Mixed Lump-Stripe Soliton Solutions to a New Extended Jimbo-Miwa Equation

“…Recently, many researchers pay more attention to the Jimbo-Miwa equation. In [25], Kaur and Wazwaz construct bilinear forms of equations (2) and (3) using truncated Painlev expansions along with the Bell polynomial approach. In [26], kink soliton, breather, and lump and line rogue wave solutions of extended (3 + 1)-dimensional Jimbo-Miwa equation are obtained by the Hirota bilinear method, whose mixed cases are discussed.…”