English
Related papers

Related papers: Normalized solution to coupled nonhomogeneous nonl…

200 papers

Motivated by the study of matter waves in Bose-Einstein condensates and coupled nonlinear optical systems, we study a system of two coupled nonlinear Schrodinger equations with inhomogeneous parameters, including a linear coupling. For that…

Dynamical Systems · Mathematics 2009-11-13 Juan Belmonte Beitia , Victor M. Perez Garcia , Pedro J. Torres

Some focusing coupled Schrodinger equations are investigated. First, existence of ground state is obtained. Second, global and non global existence of solutions are discussed via potential-well method. Finally, strong instability of…

Analysis of PDEs · Mathematics 2015-05-29 Tarek Saanouni

We obtain L2-series solutions of the nonrelativistic three-dimensional wave equation for a large class of non-central potentials that includes, as special cases, the Aharonov-Bohm, Hartmann, and magnetic monopole potentials. It also…

Quantum Physics · Physics 2009-11-10 A. D. Alhaidari

In this paper, we study the following biharmonic Schr\"odinger equation with potential and mixed nonlinearities \begin{equation*} \left\{\begin{array}{ll}\Delta^2 u +V(x,y)u+\lambda u =\mu|u|^{p-2}u+|u|^{q-2}u,\ (x, y) \in \Omega_r \times…

Analysis of PDEs · Mathematics 2024-10-02 Jun Wang , Zhaoyang Yin

We are concerned with the nonlinear Schr\"odinger equation with an $L^2$ mass constraint on both finite and locally finite graphs and prove that the equation has a normalized solution by employing variational methods. We also pay attention…

Analysis of PDEs · Mathematics 2023-02-27 Yunyan Yang , Liang Zhao

In this paper, we acquire the soliton solutions of the nonlinear Schrodinger's equation with dual power-law nonlinearity. Primiraly, we use the extended trial equation method to find exact solutions of this equation. Then, we attain some…

Mathematical Physics · Physics 2016-06-29 Hasan Bulut , Yusuf Pandir , Seyma Tuluce Demiray

Wave/Schr\"{o}dinger equations with potentials naturally originates from both the quantum physics and the study of nonlinear equations. The distractive Coulomb potential is a quantum mechanical description of distractive Coulomb force…

Analysis of PDEs · Mathematics 2024-12-04 Liang Li , Shenghao Luo , Ruipeng Shen

We study a family of separable potentials with and without added contact interactions by solving the associated Lippmann-Schwinger equation with two coupled partial waves. The matching of the resulting amplitude matrix with the…

Nuclear Theory · Physics 2024-03-11 M. S. Sánchez , J. A. Oller , D. R. Entem

A nonlinear generalisation of Schrodinger's equation had previously been obtained using information-theoretic arguments. The nonlinearities in that equation were of a nonpolynomial form, equivalent to the occurence of higher-derivative…

Quantum Physics · Physics 2015-06-26 R. Parwani , H. S. Tan

In the present paper, we study the following Schr\"{o}dinger-Maxwell equation with combined nonlinearities \begin{align*} \displaystyle - \Delta u+\lambda u+ \left(|x|^{-1}\ast |u|^2\right)u =|u|^{p-2}u +\mu|u|^{q-2}u\quad \text{in} \…

Analysis of PDEs · Mathematics 2023-09-19 Jin-Cai Kang , Yong-Yong Li , Chun-Lei Tang

An alternative approximation scheme has been used in solving the Schroedinger equation for the exponential-cosine-screened Coulomb potential. The bound state energies for various eigenstates and the corresponding wave functions are obtained…

Quantum Physics · Physics 2007-05-23 Sameer M. Ikhdair

It has been found a simple procedure for the general solution of the time-independent Schr\"odinger equation (SE) with the help of quantization of potential area in one dimension without making any approximation. Energy values are not…

Quantum Physics · Physics 2017-12-05 Hasan Hüseyin Erbil

The paper deals with the existence of standing wave solutions for the Schr\"odinger-Poisson system with prescribed mass in dimension $N=2$. This leads to investigate the existence of normalized solutions for an integro-differential equation…

Analysis of PDEs · Mathematics 2019-08-26 Silvia Cingolani , Louis Jeanjean

We consider the following coupled fractional Schr\"{o}dinger system: \begin{equation*} \left\{ \begin{aligned} &(-\Delta)^su+\lambda_1u=\mu_1|u|^{2p-2}u+\beta|v|^p|u|^{p-2}u\\ &(-\Delta)^sv+\lambda_2v=\mu_2|v|^{2p-2}v+\beta|u|^p|v|^{p-2}v\\…

Analysis of PDEs · Mathematics 2020-07-15 Meng Li , Jinchun He , Haoyuan Xu , Meihua Yang

We prove the existence of normalized ground state solutions for the biharmonic Schr\"odinger equation with combined nonlinearities and show that all ground states correspond to the local minima of the associated energy functional restricted…

Analysis of PDEs · Mathematics 2023-05-02 Xiaojun Chang , Hichem Hajaiej , Zhouji Ma , Linjie Song

Exact bound state solutions and corresponding normalized eigenfunctions of the radial Schr\"odinger equation are studied for the pseudoharmonic and Mie-type potentials by using the Laplace transform approach. The analytical results are…

Mathematical Physics · Physics 2012-03-13 Altug Arda , Ramazan Sever

We consider the cubic nonlinear Schr\"odinger equation with an exceptional potential. We obtain a sharp time decay for the global in time solution and we get the large time asymptotic profile of small solutions. We prove the existence of…

Analysis of PDEs · Mathematics 2017-07-11 Ivan Naumkin

In this paper, we report a more general class of nondegenerate soliton solutions, associated with two distinct wave numbers in different modes, for a certain class of physically important integrable two component nonlinear Schr\"{o}dinger…

Exactly Solvable and Integrable Systems · Physics 2019-12-10 S. Stalin , R. Ramakrishnan , M. Lakshmanan

This paper deals with a class of nonlinear elliptic equations involving a critical power-nonlinearity as well as a potential featuring multiple inverse square singularities. When the poles form a symmetric structure, it is natural we wonder…

Analysis of PDEs · Mathematics 2007-05-23 Veronica Felli , Susanna Terracini

In this paper, we give a complete study on the existence and non-existence of normalized solutions for Schr\"{o}dinger system with quadratic and cubic interactions. In the one dimension case, the energy functional is bounded from below on…

Analysis of PDEs · Mathematics 2021-08-24 Xiao Luo , Juncheng Wei , Xiaolong Yang , Maoding Zhen