Existence Of Periodic Wave Solutions Research Articles

Ion-acoustic stable oscillations, solitary, periodic and shock waves in a quantum magnetized electron–positron–ion plasma

Abstract Nonlinear stable oscillations, solitary, periodic and shock waves in electron–positron–ion (EPI) quantum plasma in the presence of an external static magnetic field are reported. The Korteweg-de Vries-Burgers (KdVB) equation is derived by the reductive perturbation technique (RPT). The wave solution gives shock waves depending on various parameters as quantum diffraction parameter (β), electron and positron Fermi temperatures, and densities of the system species. Amplitude, polarity, speed, and width of wave solutions are remarkably modified by species densities, kinematic viscosity, and the Bohm potential. Existence of stable oscillation of ion-acoustic waves (IAWs) is shown by using the concept of phase plane analysis. Stability of wave solution is analysed by examining the Bohm potential effect. In the absence of dissipation, phase plane of the considered plasma system is analysed to discuss the existence of periodic wave solution. The results of this study could be helpful for comprehension of the wave features in dense quantum plasmas, like white dwarfs, laboratory plasma as interaction experiments of intense laser-solid matter and microelectronic devices.

New approaches for periodic wave solutions of a non-Newtonian filtration equation with variable delay

A type of non-Newtonian filtration equations with variable delay is considered. Using a new approach which was established by Ge and Ren in (Nonlinear Anal. 58:477–488, 2004), we obtain the existence of periodic wave solutions for the non-Newtonian filtration equations. The methods of the present paper are markedly different from the existing ones.

Existence of periodic, solitary and compacton travelling wave solutions of a $$(3+1)$$-dimensional time-fractional nonlinear evolution equations with applications

In this paper, we consider the bifurcation method of dynamical systems for solving time fractional nonlinear evolution equations. We adapt and modify the methodology, incorporating new ideas from the conformable fractional derivative, to investigate exact travelling wave solutions and bifurcations of phase transitions for nonlinear evolution equations. In this study, we show the existence of periodic wave solutions, kink and anti-kink wave solutions, a bright and dark solitary wave solution and parabolic solutions. Moreover, numerical simulations method is applied to show the richer dynamical behavior of the spatial and temporal fractional order of nonlinear evolutions systems and verify the theoretical results.

Periodic wave solutions of a non-Newtonian filtration equation with an indefinite singularity

This paper is concerned with the existence of periodic wave solutions for a type of non-Newtonian filtration equations with an indefinite singularity. A sufficient criterion for the existence of periodic wave solutions for non-Newtonian filtration equation is provided via an innovative method of combining a new continuation theorem with coincidence degree theory as well as mathematical analysis skills. The novelty of the present paper is that it is the first time to discuss the existence of periodic wave solutions for the indefinite singular non-Newtonian filtration equations. Finally, two numerical examples are presented to illustrate the effectiveness and feasibility of the proposed criterion in the present paper.

Solitary Wave and Periodic Wave Solutions for a Class of Singular p-Laplacian Systems with Impulsive Effeects

This work deals with the existence of periodic wave solutions and nonexistence of solitary wave solutions for a class of second-order singular p-Laplacian systems with impulsive effects. A sufficient criterion for the solutions of the considered system is provided via an innovative method of the mountain pass theorem and an approximation technique. Some corresponding results in the literature can be enriched and extended.

EXISTENCE AND ORBITAL STABILITY OF PERIODIC WAVE SOLUTIONS FOR THE NONLINEAR SCHRÖDINGER EQUATION

In this paper, we study the existence and orbital stability of periodic wave solutions for the Schrödinger equation. The existence of periodic wave solution is obtained by using the phase portrait analytical technique. The stability approach is based on the theory developed by Angulo for periodic eigenvalue problems. A crucial condition of orbital stability of periodic wave solutions is proved by using qualitative theory of ordinal differential equations. The results presented in this paper improve the previous approach, because the proving approach does not dependent on complete elliptic integral of first kind and second kind.

Exact periodic wave solutions for the hKdV equation

In this paper, by using the Hirota bilinear method and the Jacobian theta functions for the higher order KdV equation, the existence of periodic wave solutions with one and two period are obtained. The asymptotic properties of the periodic wave solutions are analyzed in detail. It is shown that the well-known soliton solutions can be reduced from the periodic wave solutions.

A Massera Theorem for Quasi-Linear Partial Differential Equations of First Order

Massera-type criteria are derived for the existence of periodic wave solutions of quasi-linear partial differential equations of first order. Results generalize a theorem of Massera for first order scalar ordinary differential equations.