The nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov (mKdV–ZK) equation governs the behavior of weakly nonlinear ion-acoustic waves in magnetized electron–positron plasma ...which consists of equal hot and cool components of each species. By using the reductive perturbation procedure leads to a mKdV–ZK equation governing the oblique propagation of nonlinear electrostatic modes. The stability of solitary traveling wave solutions of the mKdV–ZK equation to three-dimensional long-wavelength perturbations is investigated. We found the electrostatic field potential and electric field in form traveling wave solutions for three-dimensional mKdV–ZK equation. The solutions for the mKdV–ZK equation are obtained precisely and efficiency of the method can be demonstrated.
•The hydrodynamic model is applied to three-dimensional magnetized electron–positron plasma waves.•New exact solutions for the modified Korteweg–de Vries–Zakharov–Kuznetsov equation, wave solutions, modified direct algebraic method.•We will present three traveling-wave solutions to modified Korteweg–de Vries–Zakharov–Kuznetsov equation.•We discussed the stability analysis for these solutions.
The nonlinear three-dimensional modified Zakharov–Kuznetsov (mZK) equation governs the behavior of weakly nonlinear ion-acoustic waves in a plasma comprising cold ions and hot isothermal electrons in ...a presence of a uniform magnetic field. By using the reductive perturbation procedure leads to a mZK equation governing the propagation of ion dynamics of nonlinear ion-acoustic waves in a plasma. The mZK equation has solutions that represent solitary traveling waves. We found the electrostatic field potential and electric field in form traveling wave solutions for three-dimensional mZK equation. The solutions for the mZK equation are obtained precisely and efficiency of the method can be demonstrated. The stability of solitary traveling wave solutions of the mZK equation to three-dimensional long-wavelength perturbations are investigated.
Nonlinear two-dimensional Kadomtsev–Petviashvili (KP) equation governs the behaviour of nonlinear waves in dusty plasmas with variable dust charge and two temperature ions. By using the reductive ...perturbation method, the two-dimensional dust-acoustic solitary waves (DASWs) in unmagnetized cold plasma consisting of dust fluid, ions and electrons lead to a KP equation. We derived the solitary travelling wave solutions of the two-dimensional nonlinear KP equation by implementing sech–tanh, sinh–cosh, extended direct algebraic and fraction direct algebraic methods. We found the electrostatic field potential and electric field in the form travelling wave solutions for two-dimensional nonlinear KP equation. The solutions for the KP equation obtained by using these methods can be demonstrated precisely and efficiency. As an illustration, we used the readymade package of
Mathematica
program 10.1 to solve the original problem. These solutions are in good agreement with the analytical one.
In this research work, we constructed the solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width (KP-MEW) equation with the help of new technique which is modification ...form of extended auxiliary equation mapping method. The generalized KP-MEW equation is the nonlinear PDEs which described the propagation of long-wave with dissipation and dispersion in nonlinear media. As a result, families of solitary wave solutions are obtained in different form of solitons, bright–dark solitons and traveling wave solutions. The physical structure of these new solutions is shown graphically in two and three dimensions with the aid of computer software Mathematica. These obtained new solutions show the power and effectiveness of this new method. We can also solve other nonlinear system of PDEs which are involved in mathematical physics and many other branches of physical sciences with the help of this new method.
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The propagation of three-dimensional nonlinear irrotational flow of an inviscid and incompressible fluid of the long waves in dispersive shallow-water approximation is analyzed. The problem ...formulation of the long waves in dispersive shallow-water approximation lead to fifth-order Kadomtsev-Petviashvili (KP) dynamical equation by applying the reductive perturbation theory. By using an extended auxiliary equation method, the solitary travelling-wave solutions of the two-dimensional nonlinear fifth-order KP dynamical equation are derived. An analytical as well as a numerical solution of the two-dimensional nonlinear KP equation are obtained and analyzed with the effects of external pressure flow.
In this paper we discussed analytically integrable coupled nonlinear Schrödinger Equation with Kerr law nonlinearity with the aid of newly developed technique named as extended modified auxiliary ...equation mapping method. As a result of which we have found a variety of new families of solitary wave solutions including bright, dark, half bright, half dark, combined, periodic, doubly periodic with the help of three parameters which is the key importance of this method. For physical description of our newly obtained solutions we have expressed them graphically using Mathematica 10.4 to explain more efficiently the behavior of different shapes of solutions.
•We present application in an optical fiber.•Higher order non-linear Schrödinger equation.•Optical solitary wave solutions.•The hydrodynamic mathematical methods.
In this paper, by utilizing logarithmic transformation and symbolic computation with the ansatz function technique, we investigated the rational solitons of the Fokas-Lenells equation. We obtained ...two types of M-shaped rational solitons and their dynamics are shown in figures by selecting the appropriate values of involved parameters. Furthermore, two types of interactions of M-shaped rational solitons with kink waves are investigated. We obtained the novel structures and very interesting interactional phenomena of M-shaped rational solitons with kink waves.
We investigated the new exact travelling wave solutions of the system of equations for the ion sound and Langmuir waves (SEISLWs). In this work, we use the extended form of two methods, auxiliary ...equation mapping and direct algebraic methods, to find the families of new exact travelling wave solutions of the SEISLWs. These new exact travelling solutions are derived in the form of trigonometric functions, hyperbolic functions, periodic solitary waves, bright and dark solitons, kink solutions of the SEISLWs. We used the Mathematica program to show these solutions in two and three dimensions graphically.
The derivative nonlinear Schrödinger (DNLS) equation is a nonlinear dispersive model that appears in the description of wave propagation in a plasma. The existence of a Lagrangian and the invariant ...variational principle for two coupled equations are given. The two coupled equations is describing the nonlinear evolution of the Alfvén wave with magnetosonic waves at much larger scale. A type of the coupled DNLS equations is studied by means of symbolic computation, which can describe the wave propagation in birefringent optical fibers. The functional integral corresponding to those equations is derived. We investigate the approximation solutions of the DNLS equation by choice of a trial function in the region of the rectangular box in two cases. By using this trial functions, the functional integral and the Lagrangian of the system without loss are found. The general case for the two-box potential can be obtained on the basis of a different ansatz, where we approximate the Jost function by series in the tanh function method instead of the piece-wise linear function.
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