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The purpose of this paper is to reveal dynamical behavior of nonlinear wave by searching for the new breather soliton and cross two-soliton solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG) equation.

The authors apply bilinear form and extended homoclinic test approach to the fifth-order CDG equation.

In this paper, by using bilinear form and extended homoclinic test approach, the authors obtain new breather soliton and cross two-soliton solutions of the fifth-order CDG equation. It is shown that the extended homoclinic test approach, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

The research manifests that the structures of the solution to nonlinear equations are diversified and complicated.

The methods used in this paper can be widely applied to the research of spatial and temporal characteristics of nonlinear equations in physics and engineering technology. These methods are also conducive for people to know objective laws and grasp the essential features of the development of the world.

The purpose of this paper is to reveal the dynamical behavior of higher dimensional nonlinear wave by searching for the multi-wave solutions to the (3+1)-D Jimbo-Miwa equation.

The authors apply bilinear form and extended homoclinic test approach to the (3+1)-D Jimbo-Miwa equation.

In this paper, by using bilinear form and extended homoclinic test approach, the authors obtain new cross-kink multi-soliton solutions of the (3+1)-dimensional Jimbo-Miwa equation, including the periodic breathertype of kink three-soliton solutions, the cross-kink four-soliton solutions, the doubly periodic breather-type of soliton solutions and the doubly periodic breather-type of cross-kink two-soliton solutions. It is shown that the extended homoclinic test approach, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving higher dimensional nonlinear evolution equations in mathematical physics.

The research manifests that the structures of the solution to higher dimensional nonlinear equations are diversified and complicated.

The methods used in this paper can be widely applied to the research of spatial and temporal characteristics of nonlinear equations in physics and engineering technology. These methods are also conducive for people to know objective laws and grasp the essential features of the development of the world.

The purpose of this paper is to find homoclinic breather waves, rogue waves and soliton waves for a (3 + 1)-dimensional generalized Kadomtsev–Petviashvili (gKP) equation, which can be used to describe the propagation of weakly nonlinear dispersive long waves on the surface of a fluid.

The authors apply the extended Bell polynomial approach, Hirota’s bilinear method and the homoclinic test technique to find the rogue waves, homoclinic breather waves and soliton waves of the (3 + 1)-dimensional gKP equation.

The results imply that the gKP equation admits rogue waves, homoclinic breather waves and soliton waves. Moreover, the authors also find that rogue waves can come from the extreme behavior of the breather solitary wave. The authors analyze the propagation and interaction properties of these solutions to better understand the dynamic behavior of these solutions.

These results may help us to further study the local structure and the interaction of waves in KP-type equations. It is hoped that the results can help enrich the dynamic behavior of such equations.

The purpose of this paper is to find the exact solutions of a (3 + 1)-dimensional non-integrable Korteweg-de Vries type (KdV-type) equation, which can be used to describe the stability of soliton in a nonlinear media with weak dispersion.

The authors apply the extended Bell polynomial approach, Hirota’s bilinear method and the homoclinic test technique to find the rogue waves, homoclinic breather waves and soliton waves of the (3 + 1)-dimensional non-integrable KdV-type equation. The used approach formally derives the essential conditions for these solutions to exist.

The results show that the equation exists rogue waves, homoclinic breather waves and soliton waves. To better understand the dynamic behavior of these solutions, the authors analyze the propagation and interaction properties of the these solutions.

These results may help to investigate the local structure and the interaction of waves in KdV-type equations. It is hoped that the results can help enrich the dynamic behavior of such equations.

The purpose of this paper is to obtain the nonlinear Schrodinger equation (NLSE) numerical solutions in the presence of the first-order chromatic dispersion using a second-order, unconditionally stable, implicit finite difference method. In addition, stability and accuracy are proved for the resulting scheme.

The conserved quantities such as mass, momentum and energy are calculated for the system governed by the NLSE. Moreover, the robustness of the scheme is confirmed by conducting various numerical tests using the Crank-Nicolson method on different cases of solitons to discuss the effects of the factor considered on solitons properties and on conserved quantities.

The Crank-Nicolson scheme has been derived to solve the NLSE for optical fibers in the presence of the wave packet drift effects. It has been founded that the numerical scheme is second-order in time and space and unconditionally stable by using von-Neumann stability analysis. The effect of the parameters considered in the study is displayed in the case of one, two and three solitons. It was noted that the reliance of NLSE numeric solutions properties on coefficients of wave packets drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws. Accordingly, by comparing our numerical results in this study with the previous work, it was recognized that the obtained results are the generalized formularization of these work. Also, it was distinguished that our new data are regarding to the new communications modes that depend on the dispersion, wave packets drift and nonlinearity coefficients.

The present study uses the first-order chromatic. Also, it highlights the relationship between the parameters of dispersion, nonlinearity and optical wave properties. The study further reports the effect of wave packet drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws.

The purpose of this study is to produce families of exact soliton solutions (2+1)-dimensional Korteweg-de Vries (KdV) equation, that describes shallow water waves, using an ansätze approach.

This article aims to introduce a recently developed ansätze for creating soliton and travelling wave solutions to nonlinear nonintegrable partial differential equations, especially those with physical significance.

A recently developed ansätze solution was used to successfully construct soliton solutions to the (2 + 1)-dimensional KdV equation. This straightforward method is an alternative to the Painleve test analysis, yielding similar results. The strategy demonstrated the existence of a single soliton solution, also known as a localized wave or bright soliton, as well as singular solutions or kink solitons.

The ansätze solution used to construct soliton solutions to the (2 + 1)-dimensional KdV equation is novel. New soliton solutions were also obtained.

The purpose of this paper is to introduce an approach for m‐valued classical and non‐classical (reversible and quantum) optical computing. The developed approach utilizes new multiplexer‐based optical devices and circuits within switch logic to perform the required optical computing. The implementation of the new optical devices and circuits in the optical regular logic synthesis using new lattice and systolic architectures is introduced, and the extensions to quantum optical computing are also presented.

The new linear optical circuits and systems utilize coherent light beams to perform the functionality of the basic logic multiplexer. The 2‐to‐1 multiplexer is a basic building block in switch logic, where in switch logic a logic circuit is implemented as a combination of switches rather than a combination of logic gates as in the gate logic, which proves to be less‐costly in synthesizing wide variety of logic circuits and systems. The extensions to quantum optical computing using photon spins and the collision of Manakov solitons are also presented.

New circuits for the optical realizations of m‐valued classical and reversible logic functions are introduced. Optical computing extensions to linear quantum computing using photon spins and nonlinear quantum computing using Manakov solitons are also presented. Three new multiplexer‐based linear optical devices are introduced that utilize the properties of frequency, polarization and incident angle that are associated with any light‐matter interaction. The hierarchical implementation of the new optical primitives is used to synthesize regular optical reversible circuits such as the m‐valued regular optical reversible lattice and systolic circuits. The concept of parallel optical processing of an array of input laser beams using the new multiplexer‐based optical devices is also introduced. The design of regular quantum optical systems using regular quantum lattice and systolic circuits is introduced. New graph‐based quantum optical representations using various types of quantum decision trees are also presented to efficiently represent quantum optical circuits and systems.

The introduced methods for classical and non‐classical (reversible and quantum) optical regular circuits and systems are new and interesting for the design of several future technologies that require optimal design specifications such as super‐high speed, minimum power consumption and minimum size such as in quantum computing and nanotechnology.