Abstract
The Sawada-Kotera equation with a nonvanishing boundary condition, which models the evolution of steeper waves of shorter wavelength than those depicted by the Korteweg de Vries equation, is analyzed and also the perturbed Korteweg de Vries (pKdV) equation. For this goal, a capable method known as the multiple exp-function scheme (MEFS) is formally utilized to derive the multiple soliton solutions of the models. The MEFS as a generalization of Hirota’s perturbation method actually suggests a systematic technique to handle nonlinear evolution equations (NLEEs).
Highlights
In the applied science, nonlinear evolution equations (NLEEs) are extensively used in theoretical studies to model a wide range of nonlinear phenomena
The multiple exp-function scheme (MEFS) supposes that the multisoliton solutions of NLEEs can be presented as u(x, t) = p/q in which p and q are polynomials of exponential functions
We note that multiple soliton solutions of (1) and (2) are in agreement with [19, 21, 22]
Summary
NLEEs are extensively used in theoretical studies to model a wide range of nonlinear phenomena. The MEFS supposes that the multisoliton solutions of NLEEs can be presented as u(x, t) = p/q in which p and q are polynomials of exponential functions. + b (15u3 + 15uuxx + uxxxx)x = 0 is one of NLEEs that models the evolution of steeper waves of shorter wavelength than those explained by the KdV equation and its perturbed form. By using the binary-Bell-polynomial Hirota method and symbolic computation, the bilinear form and N-soliton solutions for this model were derived in [19]. The perturbed form of KdV equation [18, 20–22]. The key goal of present work is applying the MEFS to generate the multiple soliton solutions of the models (1) and (2)
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