Application of Bifurcation Method to the Generalized Zakharov Equations

Abstract

We use the bifurcation method of dynamical systems to study the traveling wave solutions for the generalized Zakharov equations. A number of traveling wave solutions are obtained. Those solutions contain explicit periodic blow-up wave solutions and solitary wave solutions.

Analytical and Multishaped Solitary Wave Solutions for Extended Reduced Ostrovsky Equation

“…By substituting (20)- (22) into (16) and collecting all terms with the same power of ( / ) together, the left-hand sides of (16) are converted into the polynomials in ( / ). Equating the coefficients of the polynomials to zero yields a set of simultaneous algebraic equations for −1 , 0 , 1 , , , 1 , and as follows (denote for ( / )):…”

“…Recently, there are many methods being proposed to study the traveling wave solutions of nonlinear partial differential equations which are derived from physics, for example, [16][17][18][19][20][21][22][23][24][25][26][27]. As well as these methods, there are still many other methods; we cannot list all of them.…”

Topological Soliton Solution and Bifurcation Analysis of the Klein-Gordon-Zakharov Equation in(1+1)-Dimensions with Power Law Nonlinearity

“…The theory of nonlinear evolution equations (NLEEs) has come a long way in the past few decades [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. Many of the NLEEs are pretty well known in the area of theoretical physics and applied mathematics.…”

New Types of Nonlinear Waves and Bifurcation Phenomena in Schamel-Korteweg-de Vries Equation

“…According to the previous analysis, we obtain the bifurcation phase portraits of system (7) as in Figures 1 and 2. In this paper, we study the nonlinear waves and their bifurcations in (1) by using the bifurcation method of dynamical systems [21][22][23]. We point out that there are two new types of nonlinear waves, kink-like waves and compactonlike waves [24][25][26][27][28][29][30][31][32][33].…”