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1.
A complete manifold is said to be nonparabolic if it does admit a positive Green’s function. To ?nd a sharp geometric criterion for the parabolicity/nonparbolicity is an attractive question inside the function theory on Riemannian manifolds. This paper devotes to proving a criterion for nonparabolicity of a complete manifold weakened by the Ricci curvature. For this purpose, we shall apply the new Laplacian comparison theorem established by the ?rst author to show the existence of a non-constant bounded subharmonic function. 相似文献
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Gaussian-type soliton solutions of the nonlinear Schrödinger (NLS) equation with fourth order dispersion, and power law nonlinearity in the novel parity-time (${ \mathcal P }{ \mathcal T }$)-symmetric quartic Gaussian potential are derived analytically and numerically. The exact analytical expressions of the solutions are obtained in the first two-dimensional (1D and 2D) power law NLS equations. By means of the linear stability analysis, the effect of power law nonlinearity on the stability of Gauss type solitons in different nonlinear media is carried out. Numerical investigations do confirm the stability of our soliton solutions in both focusing and defocusing cases, specially around the propagation parameters. 相似文献
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The multiple lump solutions method is employed for the purpose of obtaining multiple soliton solutions for the generalized Bogoyavlensky-Konopelchenko(BK) equation. The solutions obtained contain first-order, second-order, and third-order wave solutions. At the critical point,the second-order derivative and Hessian matrix for only one point is investigated, and the lump solution has one maximum value. He's semi-inverse variational principle(SIVP) is also used for the generalized BK equation. Three major cases are studied, based on two different ansatzes using the SIVP. The physical phenomena of the multiple soliton solutions thus obtained are then analyzed and demonstrated in the figures below, using a selection of suitable parameter values.This method should prove extremely useful for further studies of attractive physical phenomena in the fields of heat transfer, fluid dynamics, etc. 相似文献
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《Physics letters. A》2020,384(28):126744
We study the influence of higher-order effects such as third order dispersion (TOD), fourth order dispersion (FOD), quintic nonlinearity (QN), self steepening (SS) and second order nonlinear dispersion (SOND) on the dynamics of dissipative soliton (DS) in metamaterials. Considering each higher-order effect as a perturbation to the system and following Lagrangian variational method, we demonstrate stable dynamics of DS as a result of the interplay between different higher-order effects. We also perform numerical analysis to confirm the analytical results. 相似文献
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The soliton molecules of the(1+1)-dimensional extended modified Korteweg–de Vries(mKdV)system are obtained by a new resonance condition, which is called velocity resonance. One soliton molecule and interaction between a soliton molecule and one-soliton are displayed by selecting suitable parameters. The soliton molecules including the bright and bright soliton, the dark and bright soliton, and the dark and dark soliton are exhibited in figures 1–3, respectively.Meanwhile, the nonlocal symmetry of the extended mKdV equation is derived by the truncated Painlevé method. The consistent Riccati expansion(CRE) method is applied to the extended mKdV equation. It demonstrates that the extended mKdV equation is a CRE solvable system. A nonauto-B?cklund theorem and interaction between one-soliton and cnoidal waves are generated by the CRE method. 相似文献
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《Physics letters. A》2020,384(11):126243
We analyze the dynamics of bright-bright solitons in two-component Bose-Einstein condensates (BECs) subject to parametric perturbations using the variational approach and direct numerical simulations. The system is described by a vector nonlinear Schrödinger equation (NLSE) appropriate to coupled multi-component BECs. A periodic variation of the inter-component coupling coefficient is used to explore nonlinear resonances and splitting of the coupled bright solitons. The analytical predictions are confirmed by direct numerical simulations of the vector NLSE. 相似文献
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