Exact 1-soliton solution of the Zakharov equation in plasmas withpower law nonlinearity

Exact traveling wave solutions to the (3+1)-dimensional mKdV–ZK and the (2+1)-dimensional Burgers equations via exp(−Φ(η))-expansion method

“…A large number of literature [9][10][11][12][13][14][15][16][17][18], where the various types of nonlinear mKdV-ZK equation and Burgers are studied and have demonstrated their analytical solutions as well as traveling wave solutions using different methods. For instance, Khan et al [47] have described the new soliton solutions of the generalized Zakharov equations using He's variational approach.…”

“…Many powerful methods to seek for exact solutions to the nonlinear partial differential equations have been proposed. Among these are the direct algebraic method [1], the Lie symmetry group method [2], the inverse scattering transform [3], the complex hyperbolic function method [4,5], the rank analysis method [6], the ansatz method [7][8][9][10][11][12][13][14][15][16][17][18], the ðG 0 =GÞ-expansion method [19][20][21][22][23][24][25][26], the modified simple equation method [27], the exp-functions method [28], the sine-cosine method [29], the Jacobi elliptic function expansion method [30,31], the F-expansion method [32], the Backlund transformation method [33], the Darboux transformation method [34], the homogeneous balance method [35][36][37], the Adomian decomposition method [38,39], the auxiliary parameter method [40], the homotopy perturbation method [41][42][43], the expðÀuðgÞÞ-expansion method [44]…”

Finite Dimensionality and Upper Semicontinuity of Kernel Sections for the Discrete Zakharov Equations

“…There are many works concerning the Cauchy problem and the initial boundary value problem of the continuous model of Zakharov equations or its related version, see [15][16][17][18][19] and the references therein. The soliton solution and numerical simulation were given to the continuous Zakharov equation with power law and dual-power law nonlinearities, see [10,27]. However, there are few papers discussing the discrete modified Zakharov equations with a quantum correction.…”

Some more similarity solutions of the(2+1)-dimensional BLP system

“…The similarity solutions obtained by using Lie-group theory may serve as a benchmark in designing, accuracy testing and comparison of numerical algorithms. Description and applications of the STM can be studied pursuing the literature [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35].…”