In this paper, we consider the final state problem for the nonlinear Schrödinger equation with
a homogeneous nonlinearity of the critical order which is not necessarily a polynomial. In …

In this paper, we consider the final state problem for the nonlinear Schrödinger equation
with a homogeneous nonlinearity which is of the long range critical order and is not …

This paper is concerned with the final state problem for the homogeneous type nonlinear
Schrödinger equation with time-decaying harmonic potentials. The nonlinearity has the …

We study the large-time behaviour of solutions of the Cauchy problem for a non-linear
Schrödinger equation. We consider the interaction between the resonance term and other …

We study the final state problem for the nonlinear Schr\"{o} dinger equation with a critical
long-range nonlinearity and a long-range linear potential. Given a prescribed asymptotic …

Рассмотрена задача Коши для нелинейного уравнения типа Соболева с кубической
нелинейностью {i∂ t (u−∂ 2 xu)+∂ 2 xu− a∂ 4 xu= u3, t> 0, x∈ R, u (0, x)= u0 (x), x∈ R …

PI Naumkin, “Logarithmic nature of the long-time asymptotics of solutions of a Sobolev-type
nonlinear equations with cubic nonlinearities”, Mat. Sb., 214:7 (2023), 134–160; Sb. Math., 214:7 …

In this note, we survey the results in the author with Masaki and Uriya [14, 17] for the final
state problem for nonlinear Schrödinger equations with critical homogeneous nonlinearity …

We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation\begin
{gather}\label {A} i\partial_ {t} u+\frac {1}{2}\partial_ {x}^{2} u-\frac {1}{4}\partial_ {x}^{4} u …

Изучено поведение при больших значениях времени решений задачи Коши для
нелинейного уравнения Шрёдингера. Рассмотрено взаимодействие резонансного …