In this research article, we study a new (3+1)-dimensional Hirota bilinear equation which can describe the dynamics of ion-acoustic wave and Alvin wave of small but finite amplitude in plasma physics and describe the propagation process of nonlinear waves in shallow water. First, we apply two methods to study the equation, namely the Hirota bilinear method and long-wave limit method M-lump solution, and line rogue waves are reported. Furthermore, we investigate the velocity, propagation trajectory, and interaction phenomenon of M-lump solution(M=2,3). Then, based on the multi-solitons, two cases of high-order breather solution are constructed by selecting some special parameters. Finally, four types interaction solutions are successfully obtained by employing long-wave limit method and selecting some special parameters. More importantly, we explore physical collision phenomenon of the interaction between nonlinear waves. In order to better illustrate the characteristics of the interaction solutions, the results are shown in three-dimensional plots and numerical simulation. To our knowledge, all of the obtained solutions in this article are novel. The results of this article may be provide an important theoretical basis for explaining some nonlinear phenomena in the field of fluid mechanics and shallow water.
相似文献Studies of the shallow water waves are active, possessing the applications in ocean engineering, marine environment, atmospheric science, etc. In this paper, we investigate a (3+1)-dimensional shallow water wave equation with time-dependent coefficients. Hirota method and symbolic computation help us work out (1) a bilinear form, (2) N-soliton solutions with N being a positive integer, (3) the higher-order breather solutions, (4) periodic-wave solutions and (5) hybrid solutions composed of one first-order breather and one soliton/two solitons. Moreover, we provide some nonlinear phenomena described by the associated solutions. All of the obtained results are determined via the time-dependent coefficients of that equation.
相似文献The fourth-order nonlinear Boussinesq water wave equation, which explains the propagation of long waves in shallow water, is explored in this article. We used the Lie symmetry approach to analyze the Lie symmetries and vector fields. Then, by using similarity variables, we obtained the symmetry reductions and soliton wave solutions. In addition, the Kudryashov method and its modification are used to explore the bright and singular solitons while the Hirota bilinear method is effectively used to obtain a form of breather and lump wave solutions. The physical explanation of the extracted solutions was shown with the free choice of different parameters by depicting some 2-D, 3-D, and their corresponding contour plots.
相似文献Under investigation is a completely generalized Hirota–Satsuma–Ito equation in (2 + 1)-dimensional. Multiple lump solutions are obtained based on three test functions, including 1-, 2- and 3-order lump solutions. Subsequently, the interaction between lump wave and solitary waves, and the interaction solution between lump wave and periodic wave are studied by using the bilinear form. Final, the stability and phase velocity are investigated. In order to analyze the dynamic behavior of these solutions, some 3D plots and contour plots are given by Mathematica.
相似文献Water waves are common phenomena in nature, which have attracted extensive attention of researchers. In the present paper, we first deduce five kinds of bilinear auto-Bäcklund transformations of the generalized (3+1)-dimensional Kadomtsev–Petviashvili equation starting from the specially exchange identities of the Hirota bilinear operators; then, we construct the N-soliton solutions and several new structures of the localized wave solutions which are studied by using the long wave limit method and the complex conjugate condition technique. In addition, the propagation orbit, velocity and extremum of the first-order lump solution on (x, y)-plane are studied in detail, and seven mixed solutions are summarized. Finally, the dynamical behaviors and physical properties of different localized wave solutions are illustrated and analyzed. It is hoped that the obtained results can provide a feasibility analysis for water wave dynamics.
相似文献In this paper, we implement the Hirota’s bilinear method to extract diverse wave profiles to the generalized perturbed-KdV equation when the test function approaches are taken into consideration. Several novel solutions such as lump-soliton, lump-periodic, single-stripe soliton, breather waves, and two-wave solutions are obtained to the proposed model. We conduct some graphical analysis including 2D and 3D plots to show the physical structures of the recovery solutions. On the other hand, this work contains a correction of previous published results for a special case of the perturbed KdV. Moreover, we investigate the significance of the nonlinearity, perturbation, and dispersion parameters being acting on the propagation of the perturbed KdV. Finally, our obtained solutions are verified by inserting them into the governing equation.
相似文献In this paper, outcomes of the study on the Bäcklund transformation, Lax pair, and interactions of nonlinear waves for a generalized (2 + 1)-dimensional nonlinear wave equation in nonlinear optics, fluid mechanics, and plasma physics are presented. Via the Hirota bilinear method, a bilinear Bäcklund transformation is obtained, based on which a Lax pair is constructed. Via the symbolic computation, mixed rogue–solitary and rogue–periodic wave solutions are derived. Interactions between the rogue waves and solitary waves, and interactions between the rogue waves and periodic waves, are studied. It is found that (1) the one rogue wave appears between the two solitary waves and then merges with the two solitary waves; (2) the interaction between the one rogue wave and one periodic wave is periodic; and (3) the periodic lump waves with the amplitudes invariant are depicted. Furthermore, effects of the noise perturbations on the obtained solutions will be investigated.
相似文献Interference wave is an important research target in the field of navigation, electromagnetic and earth science. In this work, the nonlinear property of neural network is used to study the interference wave and the bright and dark soliton solutions. The generalized broken soliton-like equation is derived through the generalized bilinear method. Three neural network models are presented to fit explicit solutions of generalized broken soliton-like equations and Boiti–Leon–Manna–Pempinelli-like equation with 100% accuracy. Interference wave solutions of the generalized broken soliton-like equation and the bright and dark soliton solutions of the Boiti–Leon–Manna–Pempinelli-like equation are obtained with the help of the bilinear neural network method. Interference waves and the bright and dark soliton solutions are shown via three-dimensional plots and density plots.
相似文献In this paper, we derive resonant and breather solutions from multi-soliton solutions of the B-type Kadomtsev–Petviashvili (BKP) equation of fourth order via the Hirota bilinear method. We first discuss N-soliton solutions of the BKP equation and use the linear superposition principle to generate N-resonant solutions. Subsequently, we construct complexiton and breather solutions and finally, study the dynamics of some selected solutions with the aid of 3D plots, contour plots and density plots.
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