Traveling wave and general form solutions for the coupled Higgs system

Abstract

In this study, the coupled Higgs system, which is a special case of the coupled Higgs field equation, which is effective in energy transport in the sub-particles of the atom, is discussed. With the help of the modified generalized exponential rational function method, which is an important instrument in obtaining traveling wave solutions, both the propagating wave solutions and general form solutions of coupled Higgs system are presented. These solutions are examined under some restrictive conditions as they are presented. It is argued that these solutions differ from the literature. The advantages and disadvantages of the method discussed in the conclusion and discussion section are discussed. In addition, the changes in the behavior of the traveling wave solution are discussed by giving physical meaning to some constants in the traveling wave solutions produced by the method. The effects on the traveling wave solution are analyzed for different values of wave number, wave velocity, and wave frequency, which have physically important meanings. In addition, the behaviors caused by these effects are supported with the help of simulation.

Complexiton, complex multiple kink soliton and the rational wave solutions to the generalized (3 + 1)-dimensional kadomtsev-petviashvili equation

“…In order to better understand and explain the nonlinear phenomena, finding exact solutions to the NPDEs has become an important focus of scholars' attention and research. In the past half century, mathematicians and physicists have been dedicated to studying exact solutions to NPDEs, including the Jacobi elliptic function expansion approach [12], modified generalized exponential rational function method [13], direct algebraic approach [14], (G'/G 2 )-expansion method [15], variational approach [16], trial-equation technique [17,18], Bäcklund transformation approach [19,20], subequation approach [21,22], Darboux transformation technique [23,24], exp-function approach [25], modified Kudryashov method [26], extended F-Expansion approach [27], sinh-Gordon equation expansion method [28] and so on. Although mathematical physicists have developed a large number of methods, it has been found that, due to the diversity and complexity of NPDEs, there is currently no unified method to solve them, and often only the corresponding methods can be selected based on specific equations.…”