In this article, we studied analytically the propagation of spiky solitary waves model by higher-order nonlinear one-dimensional K-dV equation arising in plasma physics. By using auxiliary equation mapping method, we found a series of more general and new families of solutions. These solutions are more powerful in the development of soliton dynamics, quantum plasma, adiabatic parameter dynamics, biomedical problems, fluid dynamics, industrial studies, and many other fields. The calculations are more reliable, straightforward, and effective to study analytically other nonlinear complicated physical problems. We have expressed our solutions graphically with the help of Mathematica 10.4 to understand physically the behavior of different shapes of solitary waves including kink type, anti-kink type, half bright and dark soliton.

Some new families of spiky solitary waves of one-dimensional higher-order K-dV equation with power law nonlinearity in plasma physics

In a sequel to a recent work [Das, Sarma, and Talukdar, Phys. Plasmas 5, 63 (1998)], the different nonlinear plasma-acoustic waves, based on the fluid approximation, have been derived showing the coexistences of dust-acoustic waves in plasmas contaminated by dust-charged grains. The features of the nonlinear waves, depending on the plasma composition, describe various natures of solitary waves. A new formalism, known as the tanh method and stemming from the modified simple wave solution technique, has been developed for finding the soliton propagation in the nonlinear plasma wave dynamics. The method is straightforward, with minimal mathematical manipulation, finding the heuristic formation and propagation of ion-acoustic solitary waves in the dusty plasma. The main aim is, based on the tanh method, to revisit the results in a simpler case and extending them to explain the behavior of higher-order nonlinear waves derived in generalized multicomponent plasmas. The theoretical observations highlight the sal...

A new mathematical approach for finding the solitary waves in dusty plasma

The nonlinear wave equation, derived by the augmentation of a Kadomtsev-Petviashvili (K-P) equation, discusses the evolution of soliton propagation in plasma. We employed the recently developed new formalism of a modified simple wave solution technique to the nonlinear wave dynamics for finding the soliton behaviour in plasma conceiving cold and warm electrons. Because of the new approach, the K-P wave equation has been transformed into an ordinary differential equation and finally solved by the Frobenius method in finding the nonlinear behaviours of the soliton propagation. The overall observations made by the straightforward method highlighted the various features of the solitary waves, some of which were proven to be of theoretical and experimental interest. We, in the process of using the modified simple wave solution technique, predicted the strength of the method in exhibiting the soliton dynamics having collapse or explosion causeway by the presence of multi-temperature electrons and it could be of interest by providing a better understanding in the laboratory and space plasmas.

Evolution of solitary waves in multicomponent plasmas

In this article we have discussed the analytical analysis of two dimensional modified Korteweg–de Vries (mK–dV) equation arising in plasma physics that governs the ion-acoustic solitary waves for their asymptotic behavior because of the trapping of electrons using auxiliary equation mapping method. By using this technique we have obtained some quite general and new variety of exact traveling wave solutions which are collecting some kind of semi half bright, bright, dark, semi half dark, doubly periodic, combined, periodic, half hark and half bright via three parametric values which is the primary key point of difference of our technique. These results are highly applicable to develop new theories of quantum mechanics, biomedical problems, soliton dynamics, plasma physics, nuclear physics, optical physics, fluid dynamics, electromagnetism, industrial studies, mathematical physics, biomedical problems, and in many other natural and physical sciences. For detailed physical dynamical representation of our results we have shown them with graphs in different dimensions via Mathematica 10.4 to get more understanding of different new dynamical shapes of solutions.

Study of the dynamical nonlinear modified Korteweg–de Vries equation arising in plasma physics and its analytical wave solutions

The exact multidimensional Sagdeev potential is derived in a multicomponent plasma consisting of negative ions wherein a fraction of electrons is trapped in the potential well developed in the plasma. More precisely, the Sagdeev potential equation revisits the results stemming from the Kadomtsev–Petviashvili (K–P) equation deduceable by applying the reductive perturbation technique in plasma-acoustic wave dynamics. In the study we show that the multidimensional Sagdeev potential derived here yields the formation and propagation of solitons, as well as double layers in plasma, by using a new approach known as the tanh-method to solve out the soliton phenomena. It is seen that different ordering in φ, the electrical potential, yields different solitary wave solutions that agree with earlier observations.

Quasipotential analysis for deriving the multidimensional Sagdeev potential equation in multicomponent plasma

In this paper, the various conditions under which the K-dV solitons and double layers may be formed in a plasma that includes two electron-temperatures are examined by deriving a “Further modified K-dV” (FmK-dV) equation in three dimensional space in which there is assumed to be an ambient magnetic field. Structural forms of the various ion-acoustic waves are discussed by obtaining both soliton-specific and double layer-specific solitons of the FmK-dV equation. Particular results are deduced as special cases of the more general cases.

K-dV Solitons and corresponding Double Layer Phenomena in a Plasma with Multiple Electron-Temperatures

Propagation of Multidimensional Ion‐Acoustic Waves in Multicomponent Plasmas with Negative Ions

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K-dV Solitons and corresponding Double Layer Phenomena in a Plasma with Multiple Electron-Temperatures

Propagation of Multidimensional Ion‐Acoustic Waves in Multicomponent Plasmas with Negative Ions