Stability of Algebraic Solitons for Nonlinear Schrödinger Equations of Derivative Type: Variational Approach

Hayashi, Masayuki

doi:10.1007/s00023-022-01195-9

Cited by 4 publications

(1 citation statement)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…∼ " in the notation for the (unique) holomorphic extension. Analogous ideas (holomorphic extension, uniqueness, and Bergman and Szegő spaces of holomorphic functions) were used earlier in Hayashi [35,36,37,38]. Instead of using the Green function method (cf.…”

Section: Introductionmentioning

confidence: 99%

Space-time analyticity of weak solutions to semilinear parabolic systems with variable coefficients

Baustian¹,

Takáč

2021

ejde

View full text Add to dashboard Cite

We study analytic smooth solutions of a general, strongly parabolic semilinear Cauchy problem of 2m-th order in \(\mathbb{R}^N\times (0,T)\) with analytic coefficients (in space and time variables) and analytic initial data (in space variables).They are expressed in terms of holomorphic continuation of global (weak) solutions to the system valued in a suitable Besov interpolation space of \(B^{s;p,p}\)-type at every time moment \(t\in [0,T]\). Given \(0 < T'< T\leq \infty\), it is proved that any \(B^{s;p,p}\)-type solution \(u: \mathbb{R}^N\times (0,T)\to \mathbb{C}^M\) with analytic initial data possesses a bounded holomorphic continuation \(u(x + \mathrm{i}y, \sigma + \mathrm{i}\tau)\) into a complex domain in \(\mathbb{C}^N\times \mathbb{C}\) defined by \((x,\sigma)\in \mathbb{R}^N\times (T',T)\), \(|y| < A'\) and \(|\tau | < B'\), where \(A', B'> 0\) are constants depending upon~\(T'\). The proof uses the extension of a weak solution to a \(B^{s;p,p}\)-type solution in a domain in\(\mathbb{C}^N\times \mathbb{C}\), such that this extension satisfies the Cauchy-Riemann equations. The holomorphic extension is obtained with a help from holomorphic semigroups and maximal regularity theory for parabolic problems in Besov interpolation spaces of \(B^{s;p,p}\)-type imbedded (densely and continuously) into an \(L^p\)-type Lebesgue space. Applications include \emph{risk models} for European options in Mathematical Finance. For more information see https://ejde.math.txstate.edu/special/01/b1/abstr.html

show abstract

Section: Introductionmentioning

confidence: 99%

Space-time analyticity of weak solutions to semilinear parabolic systems with variable coefficients

Baustian¹,

Takáč

2021

ejde

View full text Add to dashboard Cite

show abstract

Variational problems for the system of nonlinear Schrödinger equations with derivative nonlinearities

Hirayama,

Ikeda

2024

Calc. Var.

View full text Add to dashboard Cite

We consider the Cauchy problem of the system of nonlinear Schrödinger equations with derivative nonlinearlity. This system was introduced by Colin and Colin (Differ Int Equ 17:297–330, 2004) as a model of laser-plasma interactions. We study existence of ground state solutions and the global well-posedness of this system by using the variational methods. We also consider the stability of traveling waves for this system. These problems are proposed by Colin–Colin as the open problems. We give a subset of the ground-states set which satisfies the condition of stability. In particular, we prove the stability of the set of traveling waves with small speed for 1-dimension.

show abstract

The stability of degenerate solitons for derivative nonlinear Schrödinger equations

Kim

2024

Journal of Mathematical Analysis and Applications

View full text Add to dashboard Cite

Stability of Algebraic Solitons for Nonlinear Schrödinger Equations of Derivative Type: Variational Approach

Cited by 4 publications

References 35 publications

Space-time analyticity of weak solutions to semilinear parabolic systems with variable coefficients

Space-time analyticity of weak solutions to semilinear parabolic systems with variable coefficients

Variational problems for the system of nonlinear Schrödinger equations with derivative nonlinearities

The stability of degenerate solitons for derivative nonlinear Schrödinger equations

Contact Info

Product

Resources

About