Amin Esfahani
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View article: The Cauchy Problem for the Nonlinear Schrödinger Equation With a Convolution Potential
The Cauchy Problem for the Nonlinear Schrödinger Equation With a Convolution Potential Open
This paper investigates the nonlinear Schrödinger equation with a singular convolution potential. It demonstrates the local well‐posedness of this equation in a modified Sobolev space linked to the energy. Additionally, we derive condition…
View article: Mathematical properties of Klein–Gordon–Boussinesq systems
Mathematical properties of Klein–Gordon–Boussinesq systems Open
The Klein–Gordon–Boussinesq (KGB) system is proposed in the literature as a model problem to study the validity of approximations in the long wave limit provided by simpler equations such as KdV, nonlinear Schrödinger or Whitham equations.…
View article: Long time behavior of solutions to the generalized Boussinesq equation
Long time behavior of solutions to the generalized Boussinesq equation Open
In this paper, we investigate the generalized Boussinesq equation (gBq) as a model for the water wave problem with surface tension. Our study begins with the analysis of the initial value problem within Sobolev spaces, where we derive impr…
View article: Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction
Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction Open
In this work, we study the existence of various classes of standing waves for a nonlinear Schrödinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground‐state norm…
View article: A system of inhomogeneous NLS arising in optical media with a <inline-formula><tex-math id="M1">$ \chi^{(2)} $</tex-math></inline-formula> nonlinearity, part Ⅱ: Stability of standing waves
A system of inhomogeneous NLS arising in optical media with a nonlinearity, part Ⅱ: Stability of standing waves Open
International audience
View article: Mathematical properties of Klein-Gordon-Boussinesq systems
Mathematical properties of Klein-Gordon-Boussinesq systems Open
The Klein-Gordon-Boussinesq (KGB) system is proposed in the literature as a model problem to study the validity of approximations in the long wave limit provided by simpler equations such as KdV, nonlinear Schrödinger or Whitham equations.…
View article: Multi-soliton solutions of Klein-Gordon-Zakharov system
Multi-soliton solutions of Klein-Gordon-Zakharov system Open
In this study, we investigate the Klein-Gordon-Zakharov system with a focus on identifying multi-soliton solutions. Specifically, for a given number $N$ of solitons, we demonstrate the existence of a multi-soliton solution that asymptotica…
View article: A system of inhomogeneous NLS arising in optical media with a $ \chi^{(2)} $ nonlinearity, part Ⅰ: Dynamics
A system of inhomogeneous NLS arising in optical media with a $ \chi^{(2)} $ nonlinearity, part Ⅰ: Dynamics Open
International audience
View article: Existence of normalized ground state solution to a mixed Schrödinger system in a plane
Existence of normalized ground state solution to a mixed Schrödinger system in a plane Open
In this paper, we establish the existence of positive ground state solutions for a class of mixed Schrödinger systems with concave-convex nonlinearities in $\mathbb{R}^2$, subject to $L^2$-norm constraints; that is, \[ \left\{ \begin{align…
View article: Multi-solitons of one-dimensional Boussinesq equation
Multi-solitons of one-dimensional Boussinesq equation Open
The existence of multi-speed solitary waves for the one-dimensional good Boussinesq equation with a power nonlinearity is proven. These solutions are shown to behave at large times as a pair of scalar solitary waves traveling at different …
View article: New insights into the solutions of a class of anisotropic nonlinear Schrödinger equations on the plane
New insights into the solutions of a class of anisotropic nonlinear Schrödinger equations on the plane Open
In this paper, we study the following anisotropic nonlinear Schrödinger equation on the plane, \[ \begin{cases} {\rm i}\partial_t Φ+\partial_{xx} Φ-D_y^{2s} Φ+|Φ|^{p-2}Φ=0,&\quad (t,x,y)\in\mathbb{R} \times \mathbb{R}^2, Φ(x,y,0)=Φ_0(x,y),…
View article: Traveling waves for a nonlinear Schrödinger system with quadratic interaction in ℝ4$$ {\mathrm{\mathbb{R}}}&amp;#x0005E;4 $$
Traveling waves for a nonlinear Schrödinger system with quadratic interaction in ℝ4$$ {\mathrm{\mathbb{R}}}&#x0005E;4 $$ Open
In this paper, we consider a nonlinear Schrödinger system with quadratic interaction. We extend the recent results of Fukaya et al. (Math. Ann. 2024) and show that the system has a ground state in when the mass parameter is larger than .
View article: The Cauchy problem for the nonlinear Schrödinger equation with a convolution potential
The Cauchy problem for the nonlinear Schrödinger equation with a convolution potential Open
This paper investigates the nonlinear Schrödinger equation with a singular convolution potential. It demonstrates the local well-posedness of this equation in a modified Sobolev space linked to the energy. Additionally, we derive condition…
View article: Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction
Studies on a system of nonlinear Schrödinger equations with potential and quadratic interaction Open
In this work, we study the existence of various classes of standing waves for a nonlinear Schrödinger system with quadratic interaction, along with a harmonic or partially harmonic potential. We establish the existence of ground-state norm…
View article: On the focusing fractional nonlinear Schrödinger equation on the waveguide manifolds
On the focusing fractional nonlinear Schrödinger equation on the waveguide manifolds Open
In this paper, we consider the focusing fractional nonlinear Schrödinger equation (FNLS) on the waveguide manifolds $\mathbb{R}^d\times\mathbb{T}^m$ both in the isotropic and anisotropic case. Under different conditions, we establish the e…
View article: Angular traveling waves of the high-dimensional Boussinesq equation
Angular traveling waves of the high-dimensional Boussinesq equation Open
This paper studies traveling waves with nonzero wave speed (angular traveling waves) of the high-dimensional Boussinesq equation that have not been studied before. We analyze the properties of these waves and demonstrate that, unlike the u…
View article: Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation
Well-posedness and analyticity of solutions for the sixth-order Boussinesq equation Open
Studied in this paper is the sixth-order Boussinesq equation. We extend the local well-posedness theory for this equation with quadratic and cubic nonlinearities to the high dimensional case. In spite of having the ``bad'' fourth term $Δu$…
View article: On a system of inhomogeneous nonlinear Schrödinger equations arising in optical media with a X(2) nonlinearity
On a system of inhomogeneous nonlinear Schrödinger equations arising in optical media with a X(2) nonlinearity Open
We study a system of inhomogeneous nonlinear Schrödinger equations arising in optical media with a χ (2) nonlinearity whose local strength is subject to cusp-shaped spatial modulation, χ (2) ∼ |x| −α with α > 0, which can be induced by spa…
View article: Long time behavior of solutions to the generalized Boussinesq equation
Long time behavior of solutions to the generalized Boussinesq equation Open
In this paper, we study the generalized Boussinesq equation as a model for the water wave problem with surface tension. Initially, we investigate the initial value problem within Sobolev spaces, deriving conditions under which solutions ar…
View article: A system of inhomogeneous NLS arising in optical media with a $χ^{(2)}$ nonlinearity, part I : Dynamics
A system of inhomogeneous NLS arising in optical media with a $χ^{(2)}$ nonlinearity, part I : Dynamics Open
We study a system of inhomogeneous nonlinear Schrödinger equations that emerge in optical media with a $χ^{(2)}$ nonlinearity. This nonlinearity, whose local strength is subject to a cusp-shaped spatial modulation, $χ^{(2)}\sim |x|^{-α}$ w…
View article: A note on the quartic generalized Korteweg-de Vries equation in weighted Sobolev spaces
A note on the quartic generalized Korteweg-de Vries equation in weighted Sobolev spaces Open
In this paper we establish the persistence property for solutions of the quartic generalized Korteweg-de Vries equation with initial data in weighted Sobolev spaces $H^{s}(\mathbb{R})\cap L^2(|x|^{2r}dx)$ for $s =1/12 + \varepsilon$ and an…
View article: On the Cauchy problem for a nonlocal nonlinear Schrödinger equation
On the Cauchy problem for a nonlocal nonlinear Schrödinger equation Open
This paper considers the one-dimensional Schrödinger equation with nonlocal nonlinearity that describes the interactions of nonlinear dispersive waves. We obtain some the local well-posedness and ill-posedness result associated with this e…
View article: On the Kadomtsev-Petviashvili equation with double-power nonlinearities
On the Kadomtsev-Petviashvili equation with double-power nonlinearities Open
In this paper, we delve into the study of the generalized KP equation, which incorporates double-power nonlinearities. Our investigation covers various aspects, including the existence of solitary waves, their nonlinear stability, and inst…
View article: On the Kadomtsev-Petviashvili equation with combined nonlinearities.
On the Kadomtsev-Petviashvili equation with combined nonlinearities. Open
In this paper, we study the generalized KP equation with combined nonlinearities. First we show the existence of solitary waves of this equation. Then, we consider the associated Cauchy problem and obtain conditions under which solutions b…
View article: The time-dependent diffusion equation: An inverse diffusivity problem
The time-dependent diffusion equation: An inverse diffusivity problem Open
We find a solution of an unknown time-dependent diffusivity a(t) in a linear inverse parabolic problem by a modified genetic algorithm. At first, it is shown that under certain conditions of data, there exists at least one solution for unk…
View article: Asymptotic behavior of solutions to an evolution equation for bidirectional surface waves in a convecting fluid
Asymptotic behavior of solutions to an evolution equation for bidirectional surface waves in a convecting fluid Open
UDC 517.9 We consider the Cauchy problem for an evolution equation modeling bidirectional surface waves in a convecting fluid. We study the existence, uniqueness, and asymptotic properties of global solutions to the initial value problem a…
View article: Symmetry of the KP-type solitary waves
Symmetry of the KP-type solitary waves Open
In this paper, we study the behavior of the solitary waves of the rotation-modified Kadomtsev-Petviashvili equation. By knowing the symmetry of solitary waves in the transverse direction, we improve the previous results and show that these…
View article: Well-posedness and asymptotic behavior of the dissipative Ostrovsky equation
Well-posedness and asymptotic behavior of the dissipative Ostrovsky equation Open
In this paper we study the global well-posedness and the large-time behavior of solutions to the initial-value problem for the dissipative Ostrovsky equation. We show that the associated solutions decay faster than the solutions of the dis…
View article: GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE CAUCHY PROBLEM OF A DISSIPATIVE BOUSSINESQ-TYPE EQUATION
GLOBAL EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE CAUCHY PROBLEM OF A DISSIPATIVE BOUSSINESQ-TYPE EQUATION Open
We consider the Cauchy problem for a Boussinesq-type equation modeling bidirectional surface waves in a convecting fluid. Under small condition on the initial value, the existence and asymptotic behavior of global solutions in some time we…