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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 find solutions for the (2+1)-dimensional B-type Kadomtsev-Petviashvili equation and to research the quality of B-type Kadomtsev-Petviashvili equation.

The authors apply the extended three-wave approach and the homoclinic test technique to solve the B-type Kadomtsev-Petviashvili equation.

The authors obtain breather type of cross-kink solutions, doubly breather type of kink solitary solutions and the breather type of kink wave solutions for B-type Kadomtsev-Petviashvili equation.

As nonlinear evolution equations are characterized by rich dynamical behaviors, the authors have just found some of them and others are still to be found.

These results may help us to investigate the local structure and the interaction of waves in high-dimensional models.

The purpose of this paper is to construct analytical solutions of the (2+1)-dimensional nonlinear Schrodinger equations, and the existence of rogue waves and their localized structures are studied.

Function transformation and variable separation method are applied to the (2+1)-dimensional nonlinear Schrodinger equations.

A series of analytical solutions including rogue wave solutions for the (2+1)-dimensional nonlinear Schrodinger equations are constructed. Localized structures of rogue waves confirm the presence of large amplitude wave wall.

The localized structures of rogue waves are displayed by analytical solutions and figures. The authors just find some of them and others still to be found.

These results may help to investigate the localized structures and the behavior of rogue waves for nonlinear evolution equations. Applying two different function transformations and variable separation functions to two different states of the equations, respectively, to construct the solutions of the (2+1)-dimensional nonlinear Schrodinger equations. Rogue wave solutions are enumerated and their figures are partly displayed.

The purpose of this paper is to find new non-traveling wave solutions and study its localized structure of Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation.

The authors apply the Lie group method twice and combine with the Exp-function method and Riccati equation mapping method to the (2+1)-dimensional CDGKS equation.

The authors have obtained some new non-traveling wave solutions with two arbitrary functions of time variable.

As non-linear evolution equations is characterized by rich dynamical behavior, the authors just found some of them and others still to be found.

These results may help the authors to investigate some new localized structure and the interaction of waves in high-dimensional models. The new non-traveling wave solutions with two arbitrary functions of time variable are obtained for CDGKS equation using Lie group approach twice and combining with the Exp-function method and Riccati equation mapping method by the aid of Maple.

With the growing climate problem, it has become a consensus to develop low-carbon technologies to reduce emissions. Electric industry is a major carbon-emitting industry, accounting for 35% of global carbon emissions. Universities, as an important patent application sector in China, promote their patent application and transformation to enhance Chinese technological innovation capability. This study aims to analyze low-carbon electricity technology transformation in Chinese universities.

This paper uses IncoPat to collect patent data. The trend of low-carbon electricity technology patent applications in Chinese universities, the status, patent technology distribution, patent transformation status and patent transformation path of valid patent is analyzed.

Low-carbon electricity technology in Chinese universities has been promoted, and the number of patents has shown rapid growth. Invention patents proportion is increasing, and the transformation has become increasingly active. Low-carbon electricity technology in Chinese universities is mainly concentrated in individual cooperative patent classification (CPC) classification numbers, and innovative technologies will be an important development for electric reduction.

This paper innovatively uses valid patents to study the development of low-carbon electricity technology in Chinese universities, and defines low-carbon technology patents by CPC patent classification system. A new attempt focuses on the development status and direction in low-carbon electricity technology in Chinese universities, and highlights the contribution of valid patents to patent value.