Meromorphic solutions of nonlinear ordinary differential equations

Exact solutions of some popular nonlinear ordinary differential equations are analyzed taking their Laurent series into account. Using the Laurent series for solutions of nonlinear ordinary differential equations we discuss the nature of many methods for finding exact solutions. We show that most of these methods are conceptually identical to one another and they allow us to have only the same solutions of nonlinear ordinary differential equations

New periodic and soliton solutions by application of Exp-function method for nonlinear evolution equations

AbstractIn this letter, the Kaup–Kupershmidt, (2+1)-dimensional Potential Kadomtsev–Petviashvili (shortly PKP) equations are presented and the Exp-function method is employed to compute an approximation to the solution of nonlinear differential equations governing the problem. It has been attempted to show the capabilities and wide-range applications of the Exp-function method. This method can be used as an alternative to obtain analytic and approximate solution of different types of differential equations applied in engineering mathematics

Symbolic computation of solutions for three generalized nonlinear partial differential eQuations by using the tanh method

Three nonlinear partial differential equations, namely, the standard KdV equation, the Boussinesq equation and the generalized fifthorder KdV equation are considered here from of point the view of construct exact solutions for them. The equations that we consider here are in its most general form. New exact solutions which include periodic and soliton solutions are formally derived by using the tanh method. The programming language Matematica is used

A New Approach of Bernoulli Sub-ODE Method to Solve Nonlinear PDEs

In this paper, a new approach of the Bernoulli Sub-ODE method is proposed and this method is applied to solve the modified Liouville equation and the regularized long wave equation. As a result some new traveling wave solutions for them are successfully established. When the parameters are taken as special values, the solitary wave solutions are originated from these traveling wave solutions. Further, graphical representation of some solutions are given to visualize the dynamics of the equation. The results reveal that this method may be useful for solving higher order nonlinear partial differential equations

Traveling Wave Solutions of ZK-BBM Equation Sine-Cosine Method

Travelling wave solutions are obtained by using a relatively new technique which is called sine-cosine method for ZK-BBM equations. Solution procedure and obtained results re-confirm the efficiency of the proposed scheme

Exploring the Dynamics of Nonlocal Nonlinear Waves: Analytical Insights into the Extended Kadomtsev-Petviashvili Model

The study of nonlocal nonlinear systems and their dynamics is a rapidly increasing field of research. In this study, we take a closer look at the extended nonlocal Kadomtsev-Petviashvili (enKP) model through a systematic analysis of explicit solutions. Using a superposed bilinearization approach, we obtained a bilinear form of the enKP equation and constructed soliton solutions. Our findings show that the nature of the resulting nonlinear waves, including the amplitude, width, localization, and velocity, can be controlled by arbitrary solution parameters. The solutions exhibited both symmetric and asymmetric characteristics, including localized bell-type bright solitons, superposed kink-bell-type and antikink-bell-type soliton profiles. The solitons arising in this nonlocal model only undergo elastic interactions while maintaining their initial identities and shifting phases. Additionally, we demonstrated the possibility of generating bound-soliton molecules and breathers with appropriately chosen soliton parameters. The results of this study offer valuable insights into the dynamics of localized nonlinear waves in higher-dimensional nonlocal nonlinear models.Comment: 22 pages, 10 figures; submitted to journa

Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

The general projective Riccati equation method and the Exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term

Group Analysis and New Explicit Solutions of Simplified Modified Kawahara Equation with Variable Coefficients

The simplified modified Kawahara equation with variable coefficients is studied by using Lie symmetry method. Then we obtain the corresponding Lie algebra, optimal system, and the similarity reductions. At last, we also give some new explicit solutions for some special forms of the equations

Motions of Curves in the Projective Plane Inducing the Kaup-Kupershmidt Hierarchy

The equation of a motion of curves in the projective plane is deduced. Local flows are defined in terms of polynomial differential functions. A family of local flows inducing the Kaup-Kupershmidt hierarchy is constructed. The integration of the congruence curves is discussed. Local motions defined by the traveling wave cnoidal solutions of the fifth-order Kaup-Kupershmidt equation are described