• DIANCHEN LU

Articles written in Pramana – Journal of Physics

• New optical soliton solutions for nonlinear complex fractional Schrödinger equation via new auxiliary equation method and novel $(G^{'} / G)$-expansion method

In this research, we apply two different techniques on nonlinear complex fractional nonlinear Schrödinger equation which is a very important model in fractional quantum mechanics. Nonlinear Schrödinger equation is one of the basic models in fibre optics and many other branches of science. We use the conformable fractional derivative to transfer the nonlinear real integer-order nonlinear Schrödinger equation to nonlinear complex fractional nonlinear Schrödinger equation. We apply new auxiliary equation method and novel $(G^{'} / G)$-expansion method on nonlinear complex fractional Schrödinger equation to obtain new optical forms of solitary travelling wave solutions. We find many new optical solitary travelling wave solutions for this model. These solutions are obtained precisely and efficiency of the method can be demonstrated.

• Structure of system solutions of ion sound and Langmuir dynamical models and their applications

The present study deals with the system of equations for the ion sound and Langmuir waves (SEISLWs) by employing the extended simple equation, modified F-expansion and exp($−\Psi(\xi)$) expansion methods for constructing novel exact travelling wave solutions. Graphical simulations of some solutions are helpful to study the behaviour of SEISLWs. Hence, this approach is practically effective and productive to better understand the nonlinear problems in mathematics, physics and engineering.

• Application of mathematical methods on the system of dynamical equations for the ion sound and Langmuir 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.

• Soliton solutions of the generalised third-order nonlinear Schrödinger equation by two mathematical methods and their stability

The generalised nonlinear Schrödinger equation (NLSE) of third order is investigated, which accepts one-hump embedded solitons in a single-parameter family. In this paper, we constructed analytical solutions in the form of solitary waves and solitons of third-order NLSE by employing the extended simple equation method and exp($−\Phi(\xi)$)-expansion method. In applied physics and engineering, the obtained exact solutions have important applications. The stability of the model is examined by employing modulational instability which verifies that all the achieved exact solutions are stable. The movements of exact solitons are also presented graphically, which assist the researchers to know the physical interpretation of this complex model. Several such types of problems arising in engineering and physics can be resolved by utilising these reliable, influential and effective methods.

• Propagation of nonlinear waves with a weak dispersion via coupled (2 + 1)-dimensional Konopelchenko–Dubrovsky dynamical equation

This work applies the modified extended direct algebraic method to construct some novel exact travelling wave solutions for the coupled (2 + 1)-dimensional Konopelchenko–Dubrovsky (KD) equation. Soliton, periodic, solitary wave, Jacobi elliptic function, new elliptic, Weierstrass elliptic function solutions and so on are obtained, which have several implementations in the field of applied sciences and engineering. In addition, we discuss the dynamics of some solutions like periodic, soliton and dark-singular combo soliton by their evolutionary shapes.

• # Pramana – Journal of Physics

Volume 95, 2021
All articles
Continuous Article Publishing mode

• # Editorial Note on Continuous Article Publication

Posted on July 25, 2019