Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order

Abstract

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.

Meromorphic exact solutions of the (2 + 1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation

“…In recent years, many mathematicians and physicists studied the nonlinear integrable systems that occur in various fields such as biology, fluid dynamics, quantum and plasma physics, thermal engineering and optics. Plenty of methods have been developed for getting exact solutions to nonlinear differential equations such as the modified extended tanh method [1,2], the improved F-expansion method [3], the modified simple equation method [4], the complex method [5][6][7][8], the generalized ( ′/ ) G G -expansion method [9][10][11], the exp(− ( )) ψ z -expansion method [12][13][14][15][16], the ( + / ′) m G 1 -expansion method [17], the sine-Gordon expansion method [18][19][20][21][22][23][24], the extended sine-Gordon expansion method [25][26][27], the extended rational sinh-cosh method [28], the modified Kudryashov method [29] and other methods [30][31][32].…”

The Modulation Instability Analysis and Analytical Solutions of the Nonlinear Gross−Pitaevskii Model with Conformable Operator and Riemann Wave Equations via Recently Developed Scheme

“…This part introduces the general properties of RSGEM, First, let us consider the following sine-Gordon equation [68][69][70].…”

A Fixed Point Theorem for Time-Fractional Fornberg-Whitham Equation Arising in Atmospheric Science

“…Its non-linearity trait makes it very difficult to find an exact solution, and the discrete point findings of numerical approaches do not provide consistency. To address this problem, a number of researchers have provided techniques, such as the sine Gordon expansion method [16][17][18][19], the Homotopy analysis method [20][21], the Bernoulli sub-equation function method [22], the generalized exponential rational function method [23], the He's variational iteration method [24][25][26], the Homotopy perturbation technique [27][28][29], the Chebyshev spectral collocation method [30], the rational sine-cosine and rational sinh-cosh methods [31], the conformable derivative [32], the timefractional Caputo derivative [33], the Atangana-Baleanu derivatives [34], the fractional residual power series method [35], the Residual Power Series Method [36], semi-analytic technique to deal with nonlinear fractional differential equations [37]. For more details we can refer to [38].…”