M-lump,high-order breather solutions and interaction dynamics of a generalized $$(2 + 1)$$(2+1)-dimensional nonlinear wave equation

Nonlinear Dynamics - In this paper, a generalized $$(2+1)$$-dimensional nonlinear wave equation is obtained by extending the generalized $$(2+1)$$-dimensional Hirota bilinear equation into a more...     

Lump solutions of a ( $$2+1$$ 2 + 1 )-dimensional bSK equation

Nonlinear Dynamics - In this paper, we obtained a kind of lump solutions of ( $$2+1$$ )-dimensional bSK equation with the assistance of Mathematica by using the Hirota bilinear method. These lump...     

Riemann theta solutions and their asymptotic property for a (3 $$+$$ + 1)-dimensional water wave equation

Nonlinear Dynamics - In this paper, we consider the (3 $$+$$ 1)-dimensional water wave equation $$u_{yzt}+u_{xxxyz}-6u_{x}u_{xyz}-6u_{xy}u_{xz}=0.$$ Based on Bell polynomials, we obtain its Hirota...     

Semi-rational solutions for a $$(2+1)$$ ( 2 + 1 ) -dimensional Davey–Stewartson system on the surface water waves of finite depth

Nonlinear Dynamics - Under investigation in this work is a $$(2+1)$$ -dimensional Davey–Stewartson system, which describes the surface water wave packets of finite depth. With respect to the...     

New nonautonomous combined multi-wave solutions for ( $$\varvec{2+1}$$ 2 + 1 )-dimensional variable coefficients KdV equation

Nonlinear Dynamics - A variety of new types of nonautonomous combined multi-wave solutions of the ( $$2+1$$ )-dimensional variable coefficients KdV equation is derived by means of the generalized...     

Degeneration of solitons for a ( $$3+1$$ 3 + 1 )-dimensional generalized nonlinear evolution equation for shallow water waves

Nonlinear Dynamics - A ( $$3+1$$ )-dimensional generalized shallow water waves equation is investigated with different methods. Based on symbolic computation and Hirota bilinear form, N-soliton...     

Bilinear form,soliton, breather,lump and hybrid solutions for a ( $$\varvec{2+1}$$ 2 + 1 )-dimensional Sawada–Kotera equation

Nonlinear Dynamics - In this paper, we investigate a ( $$2+1$$ )-dimensional Sawada–Kotera (SK) equation for the atmosphere, rivers, lakes, oceans, as well as the conformal field and...     

M-lump and interactive solutions to a (3 $${+}$$ + 1)-dimensional nonlinear system

Nonlinear Dynamics - This paper aims at computing M-lump solutions for the $$(3+1)$$ -dimensional nonlinear evolution equation. These solutions in all directions decline to an identical state...     

Residual symmetry,Bäcklund transformation and CRE solvability of a ( $$\mathbf{2}{\varvec{+}}{} \mathbf{1}$$ 2 + 1 )-dimensional nonlinear system

Nonlinear Dynamics - In this paper, the truncated Painlevé expansion is employed to derive a Bäcklund transformation of a ( $$2+1$$ )-dimensional nonlinear system. This system can be...     

Topological Conjugation Classes of Tightly Transitive Subgroups of $$\text {Homeo}_{+}(\mathbb {S}^1)$$ Homeo + ( S 1 )

Journal of Dynamics and Differential Equations - Let $$\text {Homeo}_{+}(\mathbb {S}^1)$$ denote the group of orientation preserving homeomorphisms of the circle $$\mathbb {S}^1$$ . A subgroup G of...     

Painlevé analysis,auto-Bäcklund transformation and analytic solutions of a (2 $$+$$ + 1)-dimensional generalized Burgers system with the variable coefficients in a fluid

Nonlinear Dynamics - Burgers-type equations are used to describe certain phenomena in gas dynamics, traffic flow, plasma astrophysics and ocean dynamics. In this paper, a (2 $$+$$ 1)-dimensional...     

Embedded solitons in the $$(2+1)$$(2+1)-dimensional sine-Gordon equation

Nonlinear Dynamics - An effective and simple method to solve nonlinear evolution partial differential equations is the self-similarity transformation, in which one utilizes solutions of the known...     

Bäcklund transformation,multiple wave solutions and lump solutions to a (3 + 1)-dimensional nonlinear evolution equation

Nonlinear Dynamics - In this paper, a $$(3+1)$$ -dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund...     

Isochronicity for a $$\varvec{Z_{2}}$$ Z 2 -equivariant cubic system

Nonlinear Dynamics - This paper is concerned with the bi-isochronous centers problem for a cubic systems in $${Z}_2$$ -equivariant vector field. Being based on bi-centers condition, we compute the...     

Interaction of multiple superposition solutions for the $$(4 + 1)$$ ( 4 + 1 ) -dimensional Boiti-LeonManna-Pempinelli equation

Nonlinear Dynamics - Water wave is one of the most common phenomena in nature, and its involves mathematical modeling, aerodynamics, computer simulation, mechanical manufacturing, marine science...     

Unscented Kalman filter and control on $$\mathsf {TSE(3)}$$ TSE ( 3 ) with application to spacecraft dynamics

Nonlinear Dynamics - This paper presents a novel rigid-body navigation and control architecture within the framework of special Euclidean group $$\mathsf {SE(3)}$$ and its tangent bundle $$\mathsf...     

Kinematics/dynamics analysis of novel 3UPUR $${+}$$ + SP-type hybrid hand with three flexible fingers

Nonlinear Dynamics - A novel 3UPUR  $$+$$  SP-type hybrid hand with three flexible fingers is designed. Its prototype is built up, and its characteristics, DoF and constrained...     

Dobrushin States in the $${\phi^4_1}$$ Model

We consider the van der Waals free energy functional in a bounded interval with inhomogeneous Dirichlet boundary conditions imposing the two stable phases at the endpoints. We compute the asymptotic free energy cost, as the length of the interval diverges, of shifting the interface from the midpoint. We then discuss the effect of thermal fluctuations by analyzing the -measure with Dobrushin boundary conditions. In particular, we obtain a non-trivial limit in a suitable scaling in which the length of the interval diverges and the temperature vanishes. The limiting state is not translation invariant and describes a localized interface. This result can be seen as the probabilistic counterpart of the variational convergence of the associated excess free energy.     

Resonance $$\varvec{Y}$$ -type soliton,hybrid and quasi-periodic wave solutions of a generalized $$\varvec{(2+1)}$$ -dimensional nonlinear wave equation

Nonlinear Dynamics - We present a new kernel-based algorithm for modeling evenly distributed multidimensional datasets that does not rely on input space sparsification. The presented method...