Solitary Wave Ansatz Research Articles

Topological and non-topological solitons of the Klein–Gordon equations in 1+2 dimensions

This paper obtains the topological and non-topological 1-soliton solution of the Klein–Gordon equation in 1+2 dimensions. There are five various forms of this equation that will be studied. The solitary wave ansatz will be used to carry out the integration.

Soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K( m, n) equations

We consider the nonlinear dispersive K ( m , n ) equation with the generalized evolution term and derive analytical expressions for some conserved quantities. By using a solitary wave ansatz in the form of sech p function, we obtain exact bright soliton solutions for (2 + 1)-dimensional and (3 + 1)-dimensional K ( m , n ) equations with the generalized evolution terms. The results are then generalized to multi-dimensional K ( m , n ) equations in the presence of the generalized evolution term. An extended form of the K ( m , n ) equation with perturbation term is investigated. Exact bright soliton solution for the proposed K ( m , n ) equation having higher-order nonlinear term is determined. The physical parameters in the soliton solutions are obtained as function of the dependent model coefficients.

Solitary waves for nonlinear Klein–Gordon equations coupled with Born–Infeld theory

We consider the nonlinear Klein–Gordon equations coupled with the Born–Infeld theory under the electrostatic solitary wave ansatz. The existence of the least-action solitary waves is proved in both bounded smooth domain case and R3 case. In particular, for bounded smooth domain case, we study the asymptotic behaviors and profiles of the positive least-action solitary waves with respect to the frequency parameter ω. We show that when κ and ω are suitably large, the least-action solitary waves admit only one local maximum point. When ω→∞, the point-condensation phenomenon occurs if we consider the normalized least-action solitary waves.

1-Soliton solution of Benjamin–Bona–Mahoney equation with dual-power law nonlinearity

An exact 1-soliton solution of the Benjamin–Bona–Mahoney equation, with dual-power law nonlinearity, will be obtained in this paper. The solitary wave ansatz will be used to carry out this integration. This solution will also be used to evaluate a couple of integrals of motion of this equation.

Topological 1-soliton solution of the Biswas–Milovic equation with power law nonlinearity

This paper studies the topological or dark solitons due to the Biswas–Milovic equation with power law nonlinearity. The coefficients of the dispersion and nonlinearity terms are time dependent. The damping (gain) term with time-dependent coefficient is also taken into consideration. The solitary wave ansatz is used to carry out the integration. The only requirement is that the coefficient of the damping term is Riemann integrable.

Optical solitons with non-Kerr law nonlinearity and inter-modal dispersion with time-dependent coefficients

This paper studies optical solitons with non-Kerr law nonlinearity, in the presence of inter-modal dispersion. The coefficients of group velocity dispersion, nonlinearity and inter-modal dispersion terms have time-dependent coefficients. The types of nonlinearity that are considered are Kerr, power, parabolic and dual-power laws. The solitary wave ansatz is used to carry out the integration of the governing nonlinear Schrödinger’s equation with time-dependent coefficients. Both, bright and dark optical solitons, are considered, in this paper. Finally, numerical simulations are also given in each of these cases. The only necessary condition for these solitons to exist is that these time-dependent coefficients of group velocity dispersion and inter-modal dispersion are Riemann integrable.

Dark optical solitons in power law media with time-dependent coefficients

This Letter talks about the dynamics of dark optical solitons that are governed by the nonlinear Schrödinger's equation with power law nonlinearity. The solitons are considered in presence of linear attenuation, third order dispersion and self-steepening terms, all with time-dependent coefficients. The solitary wave ansatz is used to carry out the integration and an exact soliton solution is obtained. It is only necessary that these time-dependent coefficients are Riemann integrable.

Topological 1-soliton solution of Kadomtsev–Petviashvili equation with power law nonlinearity

This paper studies the Kadomtsev–Petviasvili equation with power law nonlinearity. Topological 1-soliton solution is obtained and the parameter domain is identified for these solitons to exist. The solitary wave ansatz is used to obtain this solution.

Solitary wave solution of the Zakharov–Kuznetsov equation in plasmas with power law nonlinearity

In this paper, we obtain an exact 1-soliton solution of the Zakharov–Kuznetsov equation, with power law nonlinearity, by the solitary wave ansatz method. A couple of conserved quantities of this equation are also calculated by using this 1-soliton solution.

1-soliton solution of the generalized Zakharov–Kuznetsov modified equal width equation

This paper obtains the solitary wave solution of the generalized Zakharov–Kuznetsov modified equal width equation. The solitary wave ansatz method is used to carry out the integration of this equation. A couple of conserved quantities are calculated. The domain restriction is identified for the power law nonlinearity parameter.

Solitary waves for power-law regularized long-wave equation and R(m,n) equation

This paper integrates the regularized long-wave equation with power-law nonlinearity using the solitary-wave ansatz. A few of the conserved quantities are calculated by using the 1-soliton solution. This technique is then extended to obtain the solitary-wave solution of the R(m,n) equation and a conserved quantity is also calculated for this generalized equation.

1-Soliton solution of the generalized Zakharov–Kuznetsov equation with nonlinear dispersion and time-dependent coefficients

In this Letter, the 1-soliton solution of the Zakharov–Kuznetsov equation with power law nonlinearity and nonlinear dispersion along with time-dependent coefficients is obtained. There are two models for this kind of an equation that are studied. The constraint relation between these time-dependent coefficients is established for the solitons to exist. Subsequently, this equation is again analysed with generalized evolution. The solitary wave ansatz is used to carry out this investigation.

Dynamics of solitons in plasmas for the complex KdV equation with power law nonlinearity

This paper obtains the 1-soliton solution of the complex KdV equation with power law nonlinearity. The solitary wave ansatz is used to carry out the integration. The soliton perturbation theory for this equation is developed and the soliton cooling is observed for bright solitons. Finally, the dark soliton solution is also obtained for this equation.

Topological and Non-topological Solitons for the Generalized Zakharov-Kuznetsov Modified Equal Width Equation

This paper obtains the topological and non-topological solitary wave solution of the generalized Zakharov-Kuznetsov modified equal width equation. The solitary wave ansatz method is used to carry out the integration of this equation. A couple of conserved quantities are calculated for the non-topological solitons. The domain restriction is identified for the power law nonlinearity parameter.

Optical solitons in 1+2 dimensions with non-Kerr law nonlinearity

This paper integrates the nonlinear Schrodinger’s equation in 1+2 dimensions with power and dual-power law nonlinearity. An exact 1-soliton solution is obtained in closed form using the solitary wave ansatze for these two laws. The special cases of Kerr law and parabolic law naturally fall out of these two laws.

1-soliton solution of the generalized Radhakrishnan, Kundu, Lakshmanan equation

This Letter carries out the integration of the generalized Radhakrishnan, Kundu, Lakshmanan equation to obtain the 1-soliton solution. The solitary wave ansatz is used to carry out the integration, to obtain an exact solution of this equation.

Topological and non-topological solitons of the generalized Klein–Gordon equations

This paper obtains the 1-soliton solution of five various forms of the generalized nonlinear Klein–Gordon equations. The solitary wave ansatz is used to obtain the soliton solutions of each of these cases. Both topological as well as non-topological soliton solutions are obtained depending on the type of nonlinearity in question. The conserved quantities are also calculated for each of these five forms of generalized nonlinear Klein–Gordon equations. Each of these forms reduce to the previously known results, as special cases.

Bright and dark soliton solutions for a [formula omitted] equation with t-dependent coefficients

The propagation of soliton pulses in an inhomogeneous media that is described by a K ( m , n ) equation with t-dependent coefficients is studied. By using a solitary wave ansatz in the form of sech p and tanh p functions, respectively, we obtain the exact bright and dark soliton solutions for the considered model. All the physical parameters in the solitary wave solutions are obtained as functions of the varying model coefficients. Such solutions may be useful to explain the dynamics of wave propagation in nonlinear K ( m , n ) systems exhibiting varying dispersive and nonlinear effects. Parametric conditions for the formation of soliton pulses are determined.

1-Soliton solution of Kadomtsev–Petviashvili equation with power law nonlinearity

This paper obtains the 1-soliton solution of the Kadomtsev–Petviasvili equation with power law nonlinearity using the solitary wave ansatz. An exact soliton solution is obtained and a couple of conserved quantities are also computed.

Solitary waves of Boussinesq equation in a power law media

In this paper, the solitary wave solution of the Boussinesq equation, with power law nonlinearity, is obtained by virtue of solitary wave ansatze method. The numerical simulations are obtained to support the theory.