Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order Boussinesq equation

New Exact Solutions for Generalized (3+1) Shallow Water-Like (SWL) Equation

“…Lump-type solutions and their interaction solutions are generated by Sadat [5]. In this context, various papers were presented to the literature [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The organization of this paper is as follows: firstly, we give the methodology of the improved Bernoulli sub-equation function method.…”

Singular traveling wave solutions for Boussinesq equation with power law nonlinearity and dual dispersion

“…The first term means the developing term, the first two terms form the wave operator, the term with coefficient a represents the nonlinear action, where n is the power law nonlinearity parameter. Then, the two terms with coefficients b j (j = 1, 2) are the dispersions, where the first one is the regular dispersion, while the second one arises as the surface tension [14]. Special solutions play an important role in the research of partial differential equations, and they can be used to describe and explain many phenomena in physics and engineering and so on.…”

Solitons, Shock Waves, Conservation Laws and Bifurcation Analysis of Boussinesq Equation with Power Law Nonlinearity and Dual Dispersion

“…Then, the coefficients of b j are the two dispersion terms. The coefficient of b 1 is the regular dispersion, while the second dispersion term that is given by the coefficient of b 2 accounts for the surface tension [18]. The soliton solutions to (1) will be the only issue of this paper that can be formulated only when a delicate balance between dispersion and nonlinearity is in place.…”

“…The dimensionless form of the BE with power law nonlinearity and dual-dispersion is given by [18] q tt − k 2 q xx + a q 2n xx…”

“…The dynamics of shallow water waves along ocean and sea shores are modeled by several forms of nonlinear evolution equations (NLEEs) [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22]. A few of the well-known models are Korteweg-de Vries (KdV) equation, Peregrine equation, Benjamin-Bona-Mahoney equation.…”