Journal of Nonlinear Mathematical Physics最新文献

Gradient quasi Sasaki–Ricci solitons are generalization of gradient Sasaki–Ricci solitons and Sasaki–Einstein manifolds. The main focus of this paper is to establish two gap results for the transverse Ricci curvature ({rm Ric}^{T}) and the transverse scalar curvature ({mathscr {S}}^{T}), based on which we can derive necessary and sufficient conditions for gradient quasi Sasaki–Ricci solitons to be Sasaki–Einstein. Our results generalize some recent works on this direction.

This paper studies the existence of entire radial solutions to the p-k-Hessian equation with nonlinear gradient term

and system with nonlinear gradient term

By adopting monotone iteration method, we derive the existence and asymptotic behavior of the radial solutions.

This paper investigates a class of resonance boundary value problems for Hadamard-type fractional differential equations on an infinite interval. Utilizing the Leggett-Williams norm-type theorem proposed by O’Regan and Zima, the existence of positive solutions is established. The main conclusions are illustrated with an example.

In this paper, we investigate the (2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff (gCBS) equation by using the residual symmetry analysis and consistent Riccati expansion (CRE) method, respectively. The residual symmetry of the gCBS equation is localized into a Lie point symmetry in a prolonged system and a new Bäcklund transformation of this equation is obtained. By applying the standard Lie symmetry method to the prolonged gCBS system, new symmetry reduction solutions of the gCBS equation are obtained. The gCBS equation is proved to be CRE integrable and new Bäcklund transformations of it are obtained, from which interaction solutions between solitons and periodic waves are generated and analyzed.

In this paper we discuss an improved Riemann–Hilbert method, by which arbitrary higher-order soliton solutions for the derivative nonlinear Schrödinger equation can be directly obtained. The explicit determinant form of a higher-order soliton which corresponds to one pth order pole is given. Besides the interaction related to one simple pole and the other one double pole is considered.

Analytical mechanics is the most fundamental discipline in this field. The basic principles of analytical mechanics should also be applicable to deformed objects. However, the virtual displacement principle proposed by analytical mechanics is only applicable to particle systems and rigid body systems, and not to general deformed objects. In this study, the basic principle, which includes the virtual displacement principle and d’Alembert–Lagrange principle (also called the virtual displacement principle of dynamics), of general deformed objects (such as, elastic, plastic, elasto-plastic, and flexible objects) is derived using analytical mechanics. First of all, according to the method of analytical mechanics, the external force, internal force, constraint reaction force and elastic recovery force of the deformed object system under the equilibrium state are analyzed, and the concepts of virtual displacement, ideal constraint and virtual work are introduced, and the virtual displacement principle (also called virtual work principle) of deformed objects is proposed; secondly, vector form, coordinate component form and generalized coordinate form of generalized virtual displacement principle of deformed object are given; thirdly, Introduce inertial force and use analytical mechanics to derive the d’Alembert–Lagrange principle of dynamic systems; fourthly, as application of the principle, the virtual displacement principle of deformed objects in plane polar coordinate system, space cylindrical coordinate system and spherical coordinate system are given; fifthly, the constitutive relationship between the gravitational strain of elastic–plastic materials was introduced, and an example of the application of the d'Alembert–Lagrange principle in elastic–plastic objects was given; finally, a brief conclusion is drawn. This study unifies the virtual displacement principle of elastic objects, plastic, elastoplastics, deformed object systems and rigid object systems using the basic analytical mechanics method. This is a basic principle for dealing with the static problems of deformed objects. This work also lays the foundation for further study of the dynamics of deformed object systems.

Model of the extended Dunkl oscillator based on Milovanović generalized Hermite polynomials on radial rays is discussed. Simple explicit realization of creation and annihilation operators in terms of difference-differential operators, coherent states are investigated.

In this paper we prove some Hamilton type and Li–Yau type gradient estimates on positive solutions to generalized nonlinear parabolic equations on smooth metric measure space with compact boundary. The geometry of the space in terms of lower bounds on the weighted Bakry–Émery Ricci curvature tensor and weighted mean curvature of the boundary are key in proving generalized local and global gradient estimates. Various applications of these gradient estimates in terms of parabolic Harnack inequalities and Liouville type results are discussed. Further consequences to some specific models informed by the nature of the nonlinearities are highlighted.

In this paper, we consider the asymptotic stability of the incompressible two-dimensional(2D) magnetohydrodynamic(MHD) system near the Couette flow at high Reynolds number and high magnetic Reynolds number in a finite channel (Omega =mathbb {T}times [-1,1]). We extend the results of the Navier–Stokes equations (for the previous results see[10]) to the MHD system. We prove that if the initial velocity (V_{in}) and the initial magnetic field (B_{in}) satisfy (Vert left( V_{in}-(y,0), B_{in}-(1,0)right) Vert _{H_{x,y}^{2}}le epsilon text {min}{nu ,mu }^frac{1}{2}) for some small (epsilon) independent of (nu ,mu), then the solution of the system remains within (mathcal{O}(text {min}{nu ,mu }^frac{1}{2})) of Couette flow, and close to Couette flow as (trightarrow infty); the magnetic field remains within (mathcal{O}(text {min}{nu ,mu }^frac{1}{2})) of the (1, 0), and close to (1, 0) as (trightarrow infty).