Numerous explicit soliton solutions to the fractional simplified Camassa-Holm equation through two reliable techniques

Analytical study of the propagation of nonlinear waves on a Murnaghan hyperelastic circular pipe

“…As it can be noted, both the 3D plots in Figure 4 and Figure 6 portrayed kink-typed shapes; while in Figure 5 and Figure 7, the evolution of the hyperelastic wave in the media has been captured to be increasing with an increase in the propagating time. Besides, concerned readers can equally read [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] for some of the recent proposed and deployed analytical approaches for the analytical examination of wave propagation in the contemporary nonlinear media.…”

Unveiling novel dynamics in Q-deformed Sinh-Gordon model: exploring explicit wave solutions and stability analysis

“…To study the Kundu-Mukherjee-Naskar (KMN) equation [24], the Cole-Hopf transform based method and Wang's direct mapping method were being used. Extended tanh method, ¢ ( ) G G -expansion method and the generalized exponential rational function method were utilized to find soliton solutions of NLPDEs.Closedform wave solutions of the space-time fractional simplified Camassa-Holm equation [25] were analyzed using the sine-Gordon expansion method and the extended tanh function scheme. The extraction of optical soliton solutions has also been accomplished by the extended sinh-Gordon equation expansion approach for the nonlinear Schrödinger equation [26].…”

Diverse soliton solutions to the nonlinear partial differential equations related to electrical transmission line

“…The mathematical modeling of engineering and physical problems is inherently governed by NLPDEs, which underscores the importance and intrigue of searching for closed-form wave solutions of NLPDEs. Many researchers have studied the analytical wave solutions of NLPDEs, and they've come up with lots of useful methods to solve them, such as the sine-cosine method [1], the modified simple equation technique [2], the Exp-function process [3], the modified Exp-function process [4], the nonlinear transformation method [5], the Khater method [6], He's homotopy perturbation technique [7], the variational method [8], the functional variable method [9], the extended direct algebraic method [10], the Bernoulli sub-equation function method [11], the Adomian decomposition method [12], the exp(−f(ξ)) expansion method [13], the (G G ¢ )-expansion process and its various modifications [14][15][16][17][18][19], the enhanced Kudryashov method [20], the extended tanh-function technique [21], the modified extended tanh-function procedure [22], and others [23][24][25].…”