Solitons, Rogues and Interaction Behaviors of Third-Order Nonlinear Schrodinger Equation

In this paper, we investigate the third-order nonlinear Schr\"{o}dinger equation which is used to describe the propagation of ultrashort pulses in the subpicosecond or femtosecond regime. Based on the independent transformation, the bilinear form of the third-order NLSE is constructed. The multiple soliton solutions are constructed by solving the bilinear form. The multi-order rogue waves and interaction between one-soliton and first-order rogue wave are obtained by the long wave limit in multi-solitons. The dynamics of the first-order rogue wave, second-order rogue wave and interaction between one-soliton and first-order rogue wave are presented by selecting the appropriate parameters. In particular parameters, the positions and the maximum of amplitude of rogue wave can be confirmed by the detail calculations.PACS numbers: 02.30.Ik, 05.45.Yv.

Fission and Fusion Solutions in the (2+1)-Dimensional Generalized Calogero-Bogoyavlenskii-Schiff Equation

Fission and fusion are important phenomena, which have been observed experimentally in many physical areas. In this paper, we study the above two phenomena in the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation. By introducing some new constraint conditions to its N-solitons, the fifission and fusion are obtained. Numerical figures show that the two types of solutions look like the capital letter Y in spacial structures. Then, by taking a long wave limit approach and complex conjugation restrictions, some hybrid resonance solutions are generated, such as the interaction solutions between the L-order lumps and Q-fifission (fusion) solitons, as well as hybrid solutions mixed by the T-order breathers and Q-fifission (fusion) solitons. Dynamical behaviors of these solutions are analyzed theoretically and numerically. The results obtained can be helpful for understanding the fusion and fifission phenomena in many physical models, such as the organic membrane, macromolecule material and even-clump DNA, plasmas physics and so on.

Multiple breathers and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili equation

This paper is devoted to obtaining the multi-soliton solutions, high-order breather solutions and high-order rational solutions of the (3+1)-dimensional B-type Kadomtsev–Petviashvili (BKP) equation by applying the Hirota bilinear method and the long-wave limit approach. Moreover, the interaction solutions are constructed by choosing appropriate value of parameters, which consist of four waves for lumps, breathers, rouges and solitons. Some dynamical characteristics for the obtained exact solutions are illustrated using figures.

Degeneration of Solitons for a the (3+1)-dimensional Generalized Nonlinear Evolution Equation for the Shallow Water Waves

A the (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves is investigated with different methods. Based on symbolic computation and Hirota bilinear form, Nsoliton solutions are constructed. In the process of degeneration of N-soliton solutions, T-breathers are derived by taking complexication method. Then rogue waves will emerge during the degeneration of breathers by taking the parameter limit method. Through full degeneration of N-soliton, M-lump solutions are derived based on long wave limit approach. In addition, we also find out that the partial degeneration of N-soliton process can generate the hybrid solutions composed of soliton, breather and lump.

Resonance Y-shape Solitons and Mixed Solutions for a (2+1)-dimensional Generalized Caudrey-Dodd-Gibbon-Kotera-Sawada Equation in Fluid Mechanics

Under the well-known bilinear method of Hirota, the specific expression for N-soliton solutions of (2+1)-dimensional generalized Caudrey-Dodd-Gibbon-Kotera-Sawada(gCDGKS) equation in fluid mechanics is given. By defining a noval restrictive condition on N-soliton solutions, resonant Y-type and X-type soliton solutions are generated. Under the previous new constraints, combined with the velocity resonance method and module resonant method, the mixed solutions of resonant Y-type solitons and line waves, breather solutions are found. Finally, with the support of long wave limit method, the interaction between resonant Ytype solitons and higher-order lumps is shown, and the motion trajectory equation before and after the interaction between lumps and resonant Y-type solitons is derived.

Bright--Dark Solitons in the Space-Shifted Nonlocal Coupled Nonlinear Schrodinger Equation

Multiple bright-dark soliton solutions in terms of determinants for the space-shifted nonlocal coupled nonlinear Schro¨dinger (CNLS) equation are constructed by using the bilinear (Kadomtsev-Petviashvili) KP hierarchy reduction method. It is found that the bright-dark two-soliton only occur elastic collisions. Upon their amplitudes, the bright two solitons only admit one pattern whose amplitude are equal, and the dark two solitons have three different non-degenerated patterns and two different degenerated patterns. The bright-dark four-soliton is the superposition of the two-soliton pairs and can generated bound-state solitons. The multiple double-pole bright-dark soliton solutions are generated through the long wave limit of the obtained bright-dark soliton solutions, and their collision dynamics are also investigated.PACS 02.30.Jr · 03.75.Lm · 04.20.Jb · 05.45.Yv

Short wave limit of the Novikov equation and its integrable semi-discretizations

In this paper, we are concerned with one of the generalized short wave equations proposed by Hone et al. (Lett. Math. Phys 108 927 (2018)). We show that the derivative form of this equation can be viewed as a short wave limit of the Novikov (sw-Novikov) equation. Furthermore, this generalized short wave equation and its derivative form are found to be connected to period 3 reduction of two-dimensional CKP(BKP)-Toda hierarchy, same as the short wave limit of the Depasperis-Procesi (sw-DP) equation. We propose a two-component short wave equation which contain the sw-Novikov equation and sw-DP equation as two special cases. As a main result, we construct two types of integrable semi-discretizations via Hirota’s bilinear method and provide multi-soliton solution to the semi-discrete sw-Novikov equation.

Correspondence between isoscalar monopole strengths and α inelastic cross sections on 24Mg

The correspondence between the isoscalar monopole (IS0) transition strengths and α inelastic cross sections, the B(IS0)-(α,α′) correspondence, is investigated for 24Mg(α,α′) at 130 and 386 MeV. We adopt a microscopic coupled-channel reaction framework to link structural inputs, diagonal and transition densities, for 24Mg obtained with antisymmetrized molecular dynamics to the (α,α′) cross sections. We aim at clarifying how the B(IS0)-(α,α′) correspondence is affected by the nuclear distortion, the in-medium modification to the nucleon-nucleon effective interaction in the scattering process, and the coupled-channels effect. It is found that these effects are significant and the explanation of the B(IS0)-(α,α′) correspondence in the plane wave limit with the long-wavelength approximation, which is often used, makes no sense. Nevertheless, the B(IS0)-(α,α′) correspondence tends to remain because of a strong constraint on the transition densities between the ground state and the 0+ excited states. The correspondence is found to hold at 386 MeV with an error of about 20%–30%, while it is seriously stained at 130 MeV mainly by the strong nuclear distortion. It is also found that when a 0+ state that has a different structure from a simple α cluster state is considered, the B(IS0)-(α,α′) correspondence becomes less valid. For a quantitative discussion on the α clustering in 0+ excited states of nuclei, a microscopic description of both the structure and reaction parts will be necessary.

High-order breathers and semi-rational solutions of the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation

In this paper, based on the Hirota bilinear method, the high-order breathers and interaction solutions between solitons and breathers of the (2+1)-dimensional Yu–Toda–Sasa–Fukuyama equation are investigated. The lump and semi-rational solutions are obtained by applying the long wave limit of the [Formula: see text]-soliton solution. Two types of semi-rational solutions are derived by choosing specific parameters, which are the mixture of the lump solution and solitons, and the mixture of the lump solution and breathers. Furthermore, the time evolution diagram illustrate the dynamic behavior of these solutions.