Exact solutions of the generalized multidimensional mathematical physics models via sub-equation method

Solitons and other solutions of perturbed nonlinear Biswas–Milovic equation with Kudryashov’s law of refractive index

“…The development of mathematical methods further provide us with more detailed findings for the extraction of these solitons. An effective approach to examine the exact solitons and other solutions of nonlinear models is to propose a transformation in a way to formulate at nonlinear ordinary differential equations (NODEs) that can be solved using computational techniques like modified simple equation [9], modified tanh-function method [31], sine-Gordon expansion method [2], subequation method [4], homogeneous balance method [18], new extended direct algebraic method [25], Jacobi elliptic function method [5], Riccati-Bernoulli's sub-ODE method [23], extended rational sine-cosine method [29], generalized exponential rational function method [14], functional variable method [17], and so on.…”

New Optical Solitons And Modulation Instability Analysis of Generalized Coupled Nonlinear Schrodinger-KdV System

“…Except the EshGEM and solitary wave ansatz method, analytic solutions are found to the variety of integer and fractal order models with the execution of other methods [15][16][17][18][19][20][21][22][23][24][25]. However, the proposed methods are powerful tools for constructing the exact solutions of nonlinear differential equations and gained considerable attention in recent years.…”

Stable Optical Solitons for the Higher-Order Non-Kerr NLSE via the Modified Simple Equation Method

“…Furthermore, these can be utilized to estimate the boundary data that are used in numeric and semi-analytic methods. Such techniques include the Kudryashov method and its modifications [18][19][20], functional variable method [19], generalized Riccati equation mapping method [21], Jacobi elliptic function method [21,22], sine-Gordon expansion method [23], Hirota method [24], subequation method [25], soliton ansatz method [26], G /G-expansion method [27], new extended direct algebraic method [28], extended trial function method [29], new generalized exponential rational function method [30], integral dispersion equation method [31,32], modified extended tanh-function method [33], simple equation method [34,35], and modified simple equation methods [36] (see also the references that appear therein).…”