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A novel fractional case study of nonlinear dynamics via analytical approach
The present work describes the fractional view analysis of Newell-Whitehead-Segal equations, using an innovative technique. The work is carried with...
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Local Bifurcation of Steady Almost Periodic Water Waves with Constant Vorticity
In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed. We...
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Incompressible Limit of a Fluid-Particle Interaction Model
The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method...
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Gibbs Measure for the Higher Order Modified Camassa-Holm Equation
This paper is devoted to constructing a globally rough solution for the higher order modified Camassa-Holm equation with randomization on initial...
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Efficient linear and unconditionally energy stable schemes for the modified phase field crystal equation
In this paper, we construct efficient schemes based on the scalar auxiliary variable block-centered finite difference method for the modified phase...
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Local regularity properties for 1D mixed nonlinear Schrödinger equations on half-line
The main purpose of this paper is to consider the initial-boundary value problem for the 1D mixed nonlinear Schrödinger equation u t = i αu xx + βu 2 ū x + γ ∣...
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Continuous dependence on data under the Lipschitz metric for the rotation-Camassa-Holm equation
In this article, we consider the Lipschitz metric of conservative weak solutions for the rotation-Camassa-Holm equation. Based on defining a...
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Existence of Solutions for the Semilinear Abstract Cauchy Problem of Fractional Order
In this paper we establish the existence of solutions for the nonlinear abstract Cauchy problem of order α ∈ (1, 2), where the fractional derivative...
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Stability and error estimates of the SAV Fourier-spectral method for the phase field crystal equation
We consider fully discrete schemes based on the scalar auxiliary variable (SAV) approach and stabilized SAV approach in time and the Fourier-spectral...
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Well-posedness of the Initial Value Problem for the Ostrovsky–Hunter Equation with Spatially Dependent Flux
In this paper we study the Ostrovsky–Hunter equation for the case where the flux function f ( x, u ) may depend on the spatial variable with certain...
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The Cauchy problem for the stochastic generalized Benjamin-Ono equation
The current paper is devoted to the Cauchy problem for the stochastic generalized Benjamin-Ono equation. By establishing the bilinear estimate,...
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About the solutions to the Witten–Dijkgraaf– Verlinde–Verlinde associativity equations and their Lie-algebraic and geometric properties
There is devised an algebraically feasible approach to investigating solutions to the oriented associativity equations, related with commutative and...
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Hamilton Operators and Related Integrable Differential Algebraic Novikov–Leibniz Type Structures
There is devised a general differential-algebraic approach to constructing multi-component Hamiltonian operators as classical Lie–Poisson structures...
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Local well-posedness and blow-up phenomenon for a generalization two-component Camassa–Holm system
In this paper, a new generalized two-component Camassa–Holm system is derived via the energy variational approach. This system has two parameters...
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On the Cauchy problem and peakons of a two-component Novikov system
We study a two-component Novikov system, which is integrable and can be viewed as a two-component generalization of the Novikov equation with cubic...
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A new generalised two-component Camassa–Holm type system with waltzing peakons and wave breaking
This paper mainly investigate the Cauchy problem for the generalised two-component Camassa–Holm type system, which includes the celebrated...
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Well-posedness and Dispersive/Diffusive Limit of a Generalized Ostrovsky–Hunter Equation
We consider a generalized Ostrovsky–Hunter equation and the corresponding generalized Ostrovsky one with nonlinear dispersive effects. For the first...
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The Time-Periodic Solutions to the Modified Zakharov Equations with a Quantum Correction
This paper investigates the existence and uniqueness of time-periodic solutions of the periodic initial value problem for the modified Zakharov...
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Well-posedness of the Ostrovsky–Hunter Equation under the combined effects of dissipation and short-wave dispersion
The Ostrovsky–Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution...