Results 11 to 20 of about 275,930 (166)
Multiplicity of Quasilinear Schrödinger Equation
Journal of Function Spaces, 2020 In this paper, we study the quasilinear Schrödinger equation involving concave and convex nonlinearities. When the pair of parameters belongs to a certain subset of ℝ2, we establish the existence of a nontrivial mountain pass-type solution and infinitely
Xiaorong Luo, Anmin Mao, Xiangxiang Wang
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An Existence Result for a Generalized Quasilinear Schrödinger Equation with Nonlocal Term
Journal of Function Spaces, 2020 In this paper, we consider the following generalized quasilinear Schrödinger equation with nonlocal term −divg2u∇u+gug′u∇u2+Vxu=λx−μ∗upup−2u,x∈ℝN, where N≥3, g:ℝ→ℝ+ is a C1 even function, g0=1, g′s≥0 is for all s≥0, lim∣s∣→+∞gs/sα−1≔β>0 is for some α>1 ...
Quanqing Li +3 more
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Advances in Mathematical Physics, 2018 We study the following generalized quasilinear Schrödinger equations with critical growth -divg2u∇u+gug′u∇u|2+Vxu=λfx,u+guGu|2⁎-2Gu,x∈RN, where λ>0, N≥3, g(s):R→R+ is a C1 even function, g(0)=1, and g′(s)≥0 for all s≥0, where G(u)≔∫0ug(t)dt.
Quanqing Li, Kaimin Teng, Xian Wu
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Spontaneous Collapse by Entanglement Suppression
Advanced Quantum Technologies, Volume 6, Issue 9, September 2023., 2023 The problem of quantum measurement is considered as one of the most important open questions in physics. The paper explores an alternative to the collapse postulate, which is based on a modified Schrodinger equation having a nonlinear term that gives rise to disentanglement.
Eyal Buks
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Birkhoff Normal Form and Long Time Existence for Periodic Gravity Water Waves
Communications on Pure and Applied Mathematics, Volume 76, Issue 7, Page 1416-1494, July 2023., 2023 Abstract We consider the gravity water waves system with a periodic one‐dimensional interface in infinite depth and give a rigorous proof of a conjecture of Dyachenko‐Zakharov [16] concerning the approximate integrability of these equations. More precisely, we prove a rigorous reduction of the water waves equations to its integrable Birkhoff normal ...
Massimiliano Berti +2 more
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Asymptotics of solutions to periodic problem for the Korteweg–de Vries–Burgers equation
Studies in Applied Mathematics, Volume 149, Issue 2, Page 523-536, August 2022., 2022 Abstract We consider the periodic problem for the Korteweg–de Vries–Burgers (KdVB) equation with pumping vt−vxx+α3vxxx=v+∂xv2,x∈Ω,t>0,v(0,x)=v0x,x∈Ω,\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{c}v_{t}-v_{xx}+\frac{\alpha }{3}v_{xxx}=v+\partial _{x}{\left(v^{2}\right)} ,\text{ }x\in \Omega ,t>0,\\ v(0,x)=v_{0}{\left(x\right)} ,\text{ }
Pavel I. Naumkin +1 more
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Mathematical Methods in the Applied Sciences, Volume 45, Issue 3, Page 1725-1751, February 2022., 2022 For nonlinear dispersive systems, the nonlinear Schrödinger (NLS) equation can usually be derived as a formal approximation equation describing slow spatial and temporal modulations of the envelope of a spatially and temporally oscillating underlying carrier wave.
Max Heß
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Finite‐time local piecewise control for parabolic PDEs with ODE output feedback
IET Control Theory &Applications, Volume 16, Issue 2, Page 229-243, January 2022., 2022 Abstract This paper is devoted to the finite‐time local piecewise control for parabolic partial differential equations (PDEs) by using dynamic output feedback control strategy, where the controller is designed as an ordinary differential equation (ODE).
Manna Li, Weijie Mao
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Advanced Nonlinear Studies, 2022 We study the existence of solutions for the quasilinear Schrödinger equation with the critical exponent and steep potential well. By using a change of variables, the quasilinear equations are reduced to a semilinear one, whose associated functionals ...
Xue Yan-Fang +2 more
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Advances in Mathematical Physics, Volume 2022, Issue 1, 2022., 2022 In the current work, the modified (2 + 1)‐dimensional Hietarinta model is considered by employing Hirota’s bilinear scheme. Likewise, the bilinear formalism is obtained for the considered model. In addition, the periodic‐solitary, periodic wave, cross‐kink wave, and interaction between stripe and periodic wave solutions of the mentioned equation by ...
Guangping Li +5 more
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