Dynamic properties of interactional solutions for the (4 + 1)-dimensional Fokas equation

The internal resonances between the longitudinal and transversal oscillations of a forced Timoshenko beam with an axial end spring are studied in depth. In the linear regime, the loci of occurrence of 1 : ir, \(ir \in \mathbb {N}\), internal resonances in the parameters space are identified. Then, by means of the multiple time scales method, the 1 : 2 case is investigated in the nonlinear regime, and the frequency response functions and backbone curves are obtained analytically, and investigated thoroughly. They are also compared with finite element numerical simulations, to prove their reliability. Attention is paid to the system response obtained by varying the stiffness of the end spring, and it is shown that the nonlinear behaviour instantaneously jumps from hardening to softening by crossing the exact internal resonance value, in contrast to the singular (i.e. tending to infinity) behaviour of the nonlinear correction coefficient previously observed (without properly taking the internal resonance into account).

     

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...     

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...     

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...     

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...     

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...     

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...     

Rational and complexiton solutions of the (3+1)-dimensional KP equation

In this paper, the (3+1)-dimensional KP equation is mainly discussed. Based on the Wronskian technique, the double Wronskian solution is established. Generating functions for matrix entries satisfy the linear system of partial differential equations involving free parameters. Rational, Matveev, and complexiton solutions are obtained by taking special cases in a general double Wronskian solution.     

Wronskian and Grammian solutions for the (2+1)-dimensional BKP equation

The (2 + 1)-dimensional BKP equation in the Hirota bilinear form is studied during this work. Wronskian and Grammian techniques are applied to the construction of Wronskian and Grammian solutions of this equation, respectively. It is shown that these solutions can be expressed as not only Pfaffians but also Wronskians and Grammians.     

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...     

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...     

Integrable (3+1)-dimensional Ito equation: variety of lump solutions and multiple-soliton solutions

Nonlinear Dynamics - In this work, we study an extended integrable (3+1)-dimensional Ito equation, where its complete integrability is justified via Painlevé analysis. The simplified...     

Multiwave interaction solutions for a (3+1)-dimensional nonlinear evolution equation

Nonlinear Dynamics - In this paper, by the direct algebraic method, together with the inheritance solving strategy, new types of interaction solutions among solitons, rational waves and periodic...     

Dynamics of multi-breathers,N-solitons and M-lump solutions in the (2+1)-dimensional KdV equation

Nonlinear Dynamics - The (2+1)-dimensional Korteweg–de Vries (KdV) equation is studied by distinct methods. The parameter limit method is used to derive multi-breathers solutions and lump...     

Linear superposition formula of solutions for the extended (3+1)-dimensional shallow water wave equation

Nonlinear Dynamics - Active researches on the water waves have been done, and water waves are essentially complex waves controlled by gravity field and surface tension. Using the Hirota bilinear...