Dust-acoustic solitary wave solutions for mixed nonlinearity modified Korteweg-de Vries dynamical equation via analytical mathematical methods

Structure of analytical and symbolic computational approach of multiple solitary wave solutions for nonlinear Zakharov‐Kuznetsov modified equal width equation

“…On this aspect, for the investigation of soliton solutions for NLPDEs needs the powerful and efficient methods. The lot of researcher are doing great job and have been made the different kinds of techniques such as first integral technique [25], extension of simple equation technique [26], the Hirota's direct technique [27], modify kudryashov technique [28], sine Gorden expansion technique [29], extension of auxiliary equation mapping technique [30–32], F‐expansion technique [33], $$$ \left({G}^{\prime }/G\right) $$$‐expansion technique [34], exp‐function technique [35], spectral collective technique [36], Backlund transform technique [37], tan‐cot methods [38], the extension of direct algebraic mapping technique [39–41], Binary bell polynomials technique [42], modify simple equation technique [43], modify extended auxiliary equation mapping technique [44–48], qualitative analysis technique [49], Spectral Galerkin technique [50], and Hirota bilinear technique [51].…”

Soliton molecules for combined mKdV-type bilinear equation

“…It has been applied for representing nonlinear phenomena such as transmission lines in Schottky barrier [32], acoustic waves [33], models of traffic congestion [34], Alfvén waves [35], and so on. Moreover, lots of effective mathematical techniques have been used to seek its exact solutions including soliton solutions, rational solutions, interaction solutions between cnoidal waves and kink solitary waves, among others [36][37][38][39][40][41]. While α 2 ≠ 0, equation (4) reduces to the fifth-order mKdV (mKdV-5) equation:…”