Multi-complexiton solutions of the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation

In this paper, the (2+1)-dimensional asymmetrical Nizhnik-Novikov-Veselov equation (ANNV) is investigated to acquire the complexiton solutions by the Hirota direct method. It is essential to transform the equation in to Hirota bilinear form and to build N-compilexiton solutions by pairs of conjugate wave variables.

Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation

A generalized form of (2+1)-dimensional Hirota bilinear (2D-HB) equation is considered herein in order to study nonlinear waves in fluids and oceans. The present goal is carried out through adopting the simplified Hirota’s method as well as ansatz approaches to retrieve a bunch of rational wave structures from multiple soliton solutions to breather, rational, and complexiton solutions. Some figures corresponding to a series of rational wave structures are provided, illustrating the dynamics of the obtained solutions. The results of the present paper help to reveal the existence of rational wave structures of different types for the 2D-HB equation.

The study of complexitons and periodic solitary-wave solutions with fifth-order KdV equation in (2+1) dimensions

In this paper, the generalized fifth-order (2[Formula: see text]+[Formula: see text]1)-dimensional KdV equation is scrutinized via the extended homoclinic test technique (EHTT) and extended transformed rational function (ETRF) method. With the aid of Hirota’s bilinear form, various exact solutions comprising, periodic solitary-wave, kinky-periodic solitary-wave, periodic soliton and complexiton solutions are constructed. Moreover, the mechanical features and dynamic characteristics of the obtained solutions are presented by three-dimensional plots.

Extended Transformed Rational Function Method to Nonlinear Evolution Equations

In this work, we study complexiton solutions to a (2+1)-dimensional (SK) equation and a (3+1)-dimensional nonlinear evolution equation. The complexiton solutions are combinations of trigonometric function waves and exponential function waves. For this goal, the extended transformed rational function method is carried out which is based on the Hirota bilinear forms of the considered equations and provides a systematical and convenient tool for constructing the exact solutions of nonlinear evolution equations.

Nonlinear dynamics behavior of the (2+1)-dimensional Sawada–Kotera equation

In this paper, we mainly analyze the nonlinear dynamics behavior of the (2[Formula: see text]+[Formula: see text]1)-dimensional Sawada–Kotera (S–K) equation, which can be usually used to describe shallow water phenomena from natural science. First, the multiple resonant wave and complexiton solutions are constructed with the help of the linear superposition principle, under different domain fields, such as real and complex domain fields, respectively. Next, we apply a new ansatz method to obtain a class of rogue wave solutions (one-rogue wave and two-rogue wave solutions). Finally, the 3-dimensional and 2-dimensional density graphs are plotted for the yielded results in the above texts to better illustrate the dynamics processes to them.

Optical solitons for coupled Fokas–Lenells equation in birefringence fibers

This paper discusses bright, dark and singular optical soliton as well as complexiton solutions to the coupled Fokas–Lenells equation (FLE) for birefringent fibers by three integration tools such as [Formula: see text]-expansion method, the first integral method and the sine-Gordon expansion method. The existence criterion of these solutions is also given.