General soliton solutions to a $$varvec{(2+1)}$$ ( 2 + 1 ) -dimensional nonlocal nonlinear Schrödinger equation with zero and nonzero boundary conditions

Nonlinear Dynamics - In this paper, we study the existence and bifurcation of subharmonic solutions of a four-dimensional slow–fast system with time-dependent perturbations for the...     

Families of nonsingular soliton solutions of a nonlocal Schrödinger–Boussinesq equation

Nonlocal nonlinear evolution equations with self-induced parity–time symmetric potential have received intensive attention, due to their good applications in nonlinear optics. A nonlocal Schrödinger–Boussinesq equation is proposed in this paper. By using the Hirota bilinear method and the Kadomtsev–Petviashvili hierarchy reduction method, explicit soliton solution with the nonzero boundary condition is succinctly constructed in terms of determinant. Typical dynamics and asymptotic behaviours of three types of two-soliton solutions are discussed in detail.     

Novel characteristics of lump and lump–soliton interaction solutions to the generalized variable-coefficient Kadomtsev–Petviashvili equation

Nonlinear Dynamics - With the inhomogeneities of media taken into account, a generalized variable-coefficient Kadomtsev–Petviashvili (vcKP) equation is proposed to model nonlinear waves in...     

Higher-dimensional soliton structures of a variable-coefficient Gross–Pitaevskii equation with the partially nonlocal nonlinearity under a harmonic potential

Nonlinear Dynamics - A reduction correlation between the $$(3+1)$$ -dimensional variable-coefficient Gross–Pitaevskii equation with the partially nonlocal nonlinearity under a harmonic...     

Riemann–Hilbert approach of the Newell-type long-wave–short-wave equation via the temporal-part spectral analysis

Nonlinear Dynamics - In this paper, the Riemann–Hilbert approach is systematically established for the Newell-type long-wave–short-wave equation. Firstly, we start spectral analysis...     

Mixed lump–soliton solutions to the two-dimensional Toda lattice equation via symbolic computation

Nonlinear Dynamics - Based on symbolic computation, we derive explicit rational and rational–exponential solutions to two-dimensional Toda lattice equation via the direct bilinear method. For...     

A Higdon-like non-reflecting boundary condition for the Klein–Gordon equation with evanescent waves

The non-reflecting boundary condition developed by Higdon and automated by Givoli and Neta is highly effective at absorbing propagating waves in a finite difference setting, but it does not absorb evanescent waves. In this paper, we augment the Higdon scheme with additional terms to absorb these evanescent waves in the context of the two-dimensional Klein–Gordon equation. Numerical examples illustrate the performance of this technique.     

Wavefront solutions in diffusive Nicholson’s blowflies equation with nonlocal delay

This paper is concerned with the diffusive Nicholson’s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain R.Assume that the delay kernel is a strong generic kernel.By the linear chain techniques and the geometric singular perturbation theory,the existence of travelling front solutions is shown for small delay.     

Wavefront solutions in diffusive Nicholson＇s blowflies equation with nonlocal delay

This paper is concerned with the diffusive Nicholson＇s blowflies equation with nonlocal delay incorporated as an integral convolution over the entire past time up to now and the whole one-dimensional spatial domain R. Assume that the delay kernel is a strong generic kernel. By the linear chain techniques and the geometric singular perturbation theory, the existence of travelling front solutions is shown for small delay.     

Auto-Bäcklund transformations and soliton solutions on the nonzero background for a (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation in a fluid

In this paper, a (3+1)-dimensional Korteweg-de Vries-Calogero-Bogoyavlenskii-Schif equation in a fluid is investigated. By the virtue of the truncated Painlevé expansion, a set of the auto-Bäcklund transformations of that equation is worked out. Based on the auto-Bäcklund transformations with certain non-trivial seed solutions, one-, two-, three- and N-soliton solutions on the nonzero background of that equation are derived with N as a positive integer. According to those two-soliton solutions, X- and inelastic-type soliton solutions are obtained. Via the asymptotic analysis, influence of the coefficients for the above equation is discussed and the interactions between the solitons are also studied. Then, those solitons and interactions are shown graphically.

     

Rational solutions and lump solutions to a non-isospectral and generalized variable-coefficient Kadomtsev–Petviashvili equation

Nonlinear Dynamics - In this work, a non-isospectral and variable-coefficient Kadomtsev–Petviashvili equation is considered using Hirota’s bilinear form and a direct assumption with...     

Lie symmetry analysis,soliton and numerical solutions of boundary value problem for variable coefficients coupled KdV–Burgers equation

Nonlinear Dynamics - In this article, an initial and boundary value problem for variable coefficients coupled KdV–Burgers equation is considered. With the help of Lie group approach, initial...     

Nonlinear localized waves resonance and interaction solutions of the (3 + 1)-dimensional Boiti–Leon–Manna–Pempinelli equation

Nonlinear Dynamics - This paper deals with localized waves in the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation in the incompressible fluid. Based on Hirota’s...     

Discrete bright–dark soliton solutions and parameters controlling for the coupled Ablowitz–Ladik equation

Analysis of piecewise-linear nonlinear dynamical systems is critical for a variety of civil, mechanical, and aerospace structures that contain gaps or prestress that are caused by cracks, delamination, joints or interfaces among components. Recently, a technique referred to as bilinear amplitude approximation (BAA) was developed to estimate the response of bilinear systems that have no gap or prestress. The method is based on an idea that the dynamics of a bilinear system can be treated as a combination of linear responses in two time intervals both of which the system behaves as a distinct linear system: (1) the open state and (2) the closed or sliding state. Both geometric and momentum constraints are then applied as compatibility conditions between the states to couple the linear vibrational response for each time interval. In order to estimate the response for more general cases where there are either gaps or prestress in the system, a generalized BAA method is proposed in this paper. The new method requires inclusion of contact stiffness and damping to model contact behavior in the sliding state, and new equilibrium positions for each state to establish proper coordinates. The new method also finds the bilinear frequency of the system, which cannot be computed using the bilinear frequency approximation method previously developed since that method is only accurate for the zero gap and no prestress case. The generalized BAA method is demonstrated on a single degree of freedom system, a three degree of freedom system, and a cracked cantilever beam model for various gap sizes and prestress levels.     

Interaction solutions between lump and stripe soliton to the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation

Nonlinear Dynamics - In this paper, we apply the ansatz method to the multi-linear form of the (2+1)-dimensional Date–Jimbo–Kashiwara–Miwa equation for constructing interaction...