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The paper generalizes the analytical solutions for the thermal-eigenstrain-induced elastic field in two joined half-space solids or a bimaterial with an interface of coupled dislocation-like and force-like imperfects. The present model permits quantitative jumps in displacements and/or stresses from one medium to the other. The model also leads to a set of explicit closed-form expressions for the dilatation-induced elastic fields in half-spaces I and II joined by such an imperfect interface. Cases for the elastic fields subjected to an ellipsoidal, a spherical, a spherical shell, and a cylindrical thermal inclusion are analyzed, and key results are validated by comparison with existing experimental results. The influences of several types of interfaces, such as the perfectly bonded, dislocation-like, and force-like interfaces, on the stress and displacement transmissions are further discussed.

The existence and approximation of manifolds for the Swift-Hohenberg equation with a proper parameter have mainly been studied. Using the backward-forward systems from Swift-Hohenberg equation, the existence and specific representation forms of manifolds for Swift-Hohenberg equation with a parameter have been obtained. Meanwhile, we make use of technique of deposition of lower and higher frequency spaces of solutions and assume the reduced system to obtain the main numeration approximation system of approximation solution for the original system Swift-Hohenberg equation with a proper parameter.

This paper presents the derivation of a set of the novel closed-form solutions for the eigenstrain-induced elastic fields in two joined half-space solids with an interface of coupled dislocation-like and force-like imperfects. A model is proposed to characterize the interfacial discontinuity properties concerning displacements and stresses, which permits quantitative jumps of either the displacements or the stresses from one medium to the other. Basic Galerkin vectors in these two imperfectly joined half-spaces are derived based on the boundary conditions, and thus the elastic responses are obtained in explicit expressions. Taking advantage of the three-dimensional fast Fourier Transform algorithms for the convolution and correlation, the elastic fields subjected to one arbitrarily shaped inclusion or more can be efficiently and accurately evaluated. The influences of several types of interfaces, such as the perfectly bonded interface, the dislocation-like interface, and the force-like interface, on the stress and displacement transmissions are discussed. Cases for the elastic fields due to a cuboidal, a spherical, and an array of multiple cuboidal inclusions, are investigated.

New exact solutions including bright soliton solutions, breather and periodic types of chirped soliton solutions, kink-wave and homoclinic wave solutions for the 2D Ginzburg–Landau equation are obtained using the special envelope transform and the auxiliary function method. It is shown that the specially envelope transform and the auxiliary function method provide a powerful mathematical tool for solving nonlinear equations arising in mathematical physics.

Two types of soliton deflexion of (1 + 3)D Kadomtsev–Petviashvili (K–P) equation are considered. Using the Hirota bilinear form and the new technique of “homoclinic test”, a type of exact periodic soliton solution of the K–P equation with positive transverse dispersion effects is obtained. Another type of periodic soliton solution is found by means of the periodic soliton solution of the K–P equation with negative transverse dispersion effects and a temporal and spatial transformation. It is also investigated that the equilibrium solution u 0 = - 1 6 is an unique deflexion point, periodic soliton of traveling in different spatial directions will be interchanged with the solution varying from one side of - 1 / 6 to the other side.

Exact solitary-wave, kink wave and singular solitary-wave solutions for Kadomtsev–Petviashvili (KP) equation with p-power (p > 1) of nonlinearity are obtained using a novel auxiliary equation and homogeneous balance method.

New exact wave solutions including homoclinic wave, kink wave and soliton solutions for the 2D Ginzburg–Landau equation are obtained using the auxiliary function method, generalized Hirota method and the ansatz function technique under the certain constraint conditions of coefficients in equation, respectively. The result shows that there exists a kink-wave solution which tends to one and the same periodic wave solution as time tends to infinite.

In this paper, we obtain a new class of exact cross kink-wave and periodic solitary-wave solutions for Jimbo–Miwa equation by using two-soliton method, bilinear method and transforming parameters into complex ones. Moreover, we investigate singular and non-singular phenomenons of solutions. In addition, we study the resonance and non-resonance interactions between y – t periodic solitons and different line solitons.