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...     

Wronskian,Pfaffian and periodic wave solutions for a $$(2 + 1)$$ ( 2 + 1 ) -dimensional extended shallow water wave equation

Nonlinear Dynamics - Under investigation in this paper is a $$(2 + 1)$$ -dimensional extended shallow water wave equation. Bilinear form is obtained via the generalized dependent variable...     

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...     

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...     

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...     

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...     

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...     

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...     

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...     

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...     

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...     

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...     

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.     

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...     

Reflector Problem in $${\mathbb R^n}$$ Endowed with Non-Euclidean Norm

In this paper, we establish existence and uniqueness up to dilations for the reflector problem in a nonisotropic medium in for which light wavefronts are described by non-Euclidean norm spheres, through approaches of paraboloid approximation and optimal mass transport. Research of L. A. Caffarelli supported in part byNSF grant No. DMS-0140338; research of Q. Huang supported in part by NSF grants No. DMS-0201599 and No. DMS-0502045.     

Interactions of the vector breathers for the coupled Hirota system with $$4\times 4$$ 4 × 4 Lax pair

Nonlinear Dynamics - In this paper, we investigate the interactions of the vector breathers for the coupled Hirota system with $$4\times 4$$ Lax pair. Firstly, we give the first-order breather...     

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...     

Stable and oscillating solitons of $$\pmb {\mathcal {PT}}$$ -symmetric couplers with gain and loss in fractional dimension

Nonlinear Dynamics - Families of coupled solitons of $$\mathcal {PT}$$ -symmetric physical models with gain and loss in fractional dimension and in settings with and without cross-interactions...     

Flow Visualization of Superbursts and of the Log-Layer in a DNS at $$ \operatorname{Re} _{\tau } = 950 $$

This paper uses direct numerical simulations (DNS) of turbulent flow in a channel at (Del álamo, Jiménez, Zandonade, Moser J Fluid Mech 500:135–144, 2004) to provide a picture of the turbulent structures making large contributions to the Reynolds shear stress. Considerable work of this type has been done for the viscous wall region at smaller , for which a log-layer does not exist. Recent PIV measurements of turbulent velocity fluctuations in a plane parallel to the direction of flow have emphasized the dominant contribution of large scale structures in the outer flow. This prompted Hanratty and Papavassiliou (The role of wall vortices in producing turbulence. In: Panton, R.L. (ed) Self-sustaining Mechanism of Wall Turbulence. Computational Mechanics Publications, Southampton, pp. 83–108, 1997) to use DNS at to examine these structures in a plane perpendicular to the direction of flow. They identified plumes which extend from the wall to the center of a channel. The data at are used to explore these results further, to examine the structure of the log-layer, and to test present notions about the viscous wall layer.