Stable solutions to the nonlinear RLC transmission line equation and the Sinh–Poisson equation arising in mathematical physics

Abstract

The Sinh–Poisson equation and the RLC transmission line equation are important nonlinear model equations in the field of engineering and power transmission. The modified simple equation (MSE) procedure is a realistic, competent and efficient mathematical scheme to ascertain the analytic soliton solutions to nonlinear evolution equations (NLEEs). In the present article, the MSE approach is put forward and exploited to establish wave solutions to the previously referred NLEEs and accomplish analytical broad-ranging solutions associated with parameters. Whenever parameters are assigned definite values, diverse types of solitons originated from the general wave solutions. The solitons are explained by sketching three-dimensional and two-dimensional graphs, and their physical significance is clearly stated. The profiles of the attained solutions assimilate compacton, bell-shaped soliton, peakon, kink, singular periodic, periodic soliton and singular kink-type soliton. The outcomes assert that the MSE scheme is an advance, convincing and rigorous scheme to bring out soliton solutions. The solutions obtained may significantly contribute to the areas of science and engineering.

Bright, periodic, compacton and bell-shape soliton solutions of the extended QZK and (3 + 1)-dimensional ZK equations

“…Thus, different methods are used to search soliton solutions to these NLEEs. Some of them are the extended simple equation technique [3], the generalized Kudryashov technique [4], the first-integral technique [5], the new auxiliary equation technique [6], the Bernoulli sub-equation function technique [7,8], the Riccati-Bernoulli sub-ODE method [9][10][11], the sine-Gordon expansion technique [12,13], the sine-cosine technique [14], the generalized unified technique [15], the modified Khater method [16], the tanh-coth method [17], He's variational principle [18,19], the B ä cklund transformation method [20], the unified Riccati equation expansion method [21], the extended Kudryashov method [22], the improved ( ) / ¢ G G -expansion method [23], the functional variable method [24], the exp-expansion technique [25], the improved F-expansion technique [26], the MSE technique [27][28][29][30], the enhanced MSE method [31], the Jacobi elliptic functions method [32][33][34][35], and other different techniques [36][37][38][39][40].…”