A novel analytical solution for the modified Kawahara equation using the residual power series method

Exact traveling wave solutions of the space–time fractional complex Ginzburg–Landau equation and the space-time fractional Phi-4 equation using reliable methods

“…(7) can be computed by balancing the highest-order nonlinear term with the highest-order derivative in u(ξ ) occurring in Eq. (6). If the degree of u(ξ ) is Deg[u(ξ )] = N , then the degree of the other terms can be expressed as…”

“…Seadawy employed the reductive perturbation method to construct solitary traveling wave solutions of the two-dimensional nonlinear Kadomtsev-Petviashvili (KP) dynamic equation in dust-acoustic plasmas [4] and the nonlinear threedimensional modified Zakharov-Kuznetsov (mZK) equation [5]. Mahmood and Yousif found novel analytical solutions for the modified Kawahara equation using the residual power series method [6]. Seadawy applied the auxiliary equation of the direct algebraic method to construct traveling wave solutions of the higher-order nonlinear Schrödinger equation [7].…”

Jacobi Elliptic Function Solutions and Traveling Wave Solutions of the (2 + 1)‐Dimensional Gardner‐KP Equation

“…It is arrested that all these techniques are based on problems, that is to say, some methods operate well with issues that have been affected, but not with others. Many well‐known models have been developed to describe the dynamics of nonlinear waves that have emerged in the recent area of modern science and engineering, such as the equation Kortewegde Vries (KdV), Kortewegde Vries Burgers equation, modified Kortewegde Vries (mKdV) equation, modified Kortewegde Vries KadomtsevPetviashvili (mKdVKP) equation, Boussinesq equation, Zakharov‐Kuznetsov‐Burgers equation, modified Kortewegde Vries ZakharovKuznetsov equation, Perergrine equation, Kawahara equation, BenjaminBonaMahoney equation, Kadomtsev PetviashviliBenjaminBonaMahony (KPBBM) equation, coupled Kortewegde Vries equation, coupled Boussinesq equation, Gardner equation, a combination of KdV and mKdV equations. Some of these techniques are used by distinct authors to discover the solitary waves solution of nonlinear evolution equations, these methods include: the modified extended mapping method, tanhsech method and the extended tanhcoth method, Kudryashov method, expansion method, auxiliary equation method, inverse scattering transform method, first integral method, Jacobi elliptic function method, modified simple equation method, lumped Galerkin method, extended simple equation method, homogeneous balance method, Darboux transformation, Backland transformation and modified extended direct algebraic method .…”

Analytical Solution for the Time Fractional BBM‐Burger Equation by Using Modified Residual Power Series Method

“…Recently, an analytical method based on power series expansion without linearization, discretization, or perturbation has been introduced and successfully applied to many kinds of fractional differential equations arising in strongly nonlinear and dynamic problems. The method was named residual power series method (RPSM) [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], which was used to find the analytical solution for several classes of time fractional differential equations. The residual power series method has been widely used in different fields.…”

“…In [15][16][17][18][19][20][21], residual power series method, as a powerful method, was used to solve the other time fractional differential equations. Residual power series method was also used for the time fractional Gardner [23] and Kawahara equations in [22], the time fractional Phi-4 equation in [24], the fractional population diffusion model [25], the generalized Burger-Huxley equation [26], and the time fractional two-component evolutionary system of order 2 [27].…”