Specific wave profiles and closed-form soliton solutions for generalized nonlinear wave equation in (3+1)-dimensions with gas bubbles in hydrodynamics and fluids

Analytical Soliton Solutions of the Coupled Radhakrishnan‐Kundu‐Lakshmanan Equation via Three Techniques

“…Step 3. Putting (10), (11), and ( 13) into (4), we acquire a polynomial of QðηÞ. Gathering all terms with the like powers of QðηÞ with each other's and setting each coefficient to zero, we get a set of algebraic equations.…”

“…Solutions through the Generalized Kudryashov Method. From (10), the solution of ( 23) can be written in the form:…”

“…The theory and investigation of soliton solutions is one of the important research fields relating to nonlinear partial differential equations ascending in telecommunication engineering, optics, mathematical physics, and other domains of nonlinear sciences. Therefore, diverse academics and researchers developed a number of numerical and analytical techniques, namely, the ðm + 1/G ′ Þ-expansion technique [1], the truncated M-fractional derivative scheme [2], the q-homotopy analysis technique [3], Atangana-Baleanu operator scheme [4], the improved Bernoulli subequation function process [5], the sine-Gordon expansion approach [6], the Haar wavelet technique [7], the biframelet systems process [8], the Lie symmetry technique [9], the generalized exponential rational function mode [10], the Painlevé analysis [11], the extended subequation method [12], the improved ðG′/GÞ-expansion scheme [13], the Hirota simplified method [14], the onedimensional subalgebra system [15], Painlevé analysis and multi-soliton solutions technique [16], the one-parameter Lie group of transformations approach [17], etc.…”

Dynamical behavior for the approximate solutions and different wave profiles nonlinear fractional generalised Pochhammer-Chree equation in mathematical physics

“…First,ourself receive the solutions for existence and uniqueness. And other research solved timefractional generalised analytical-approximate solutions PC equations for waves publicity of an elastic rod using the q-homotopy analysis of the transform method [13][14][15], Modulation instability analysis [16], Hydro-magnetic [17], solitary wave [18], Carreau fluid [19], kink wave [20], Existence and Uniqueness [21,24], Hilbert space [22], natural reduced differential transform method [23], iterative Laplace transform method [25], tanh-coth and the sine-cosine methods [26], explicit fourthorder time stepping methods [27], decomposition method [28], weierstrass elliptic function method [30], modified F-expansion methods [31], global existence [32], generalized exponential rational function (GERF) technique [33][34], bernoulli sub-equation function method [35], lie group method [36], fractional natural decomposition method [37], modified exponential method [39], residual power series method [40], adams-bashforth scheme [41], laplace transform [42][43], conformable derivative [44,47], Mittag-Leffler function [45], caputo derivatives [46], Sumudu transform [48],and so on [49][50][51][52][53]…”

New Solutions for IOPM and (3+1)-Dimensional NLWE in Liquid with Gas Bubbles

“…In the area of liquid with gas bubbles, bubble-liquid mixing equations have been improved to identify the propagation of weak nonlinear waves which are extensively observed in natural science, hydrodynamics, medical science, and engineering. Motivated by that, (3+1)-dimensional NLWE in liquid with gas bubbles is tackled as (Wang et al, 2019;Wang et al, 2020;Kumar et al,2021;Shen et al, 2022;Yadav and Arora, 2021;Tu et al, 2016;,…”