The fractional modified Zakharov system for plasmas with a quantum correction

Abstract

In this paper, we consider the fractional modified Zakharov system with a quantum correction. This system can be regarded as a generalization of the Garcia model to the fractional order. By the properties of the fractional Sobolev spaces and a priori estimates, we overcome the mathematical difficulty arising in the fractional model and establish the global existence and uniqueness of the solution.

Conservative Fourier spectral method for a class of modified Zakharov systems with high-order space fractional quantum correction $\dagger$

“…are developed for the space fractional Schrödinger equations [21][22][23][24][25][26][27][28][29][30][31][32], space fractional Klein-Gordon-Schrödinger equations [33][34][35][36] and space fractional Klein-Gordon-Zakharov equations [37] with zeros boundary condition or periodic boundary condition. In this paper, we consider the modified Zakharov system with high-order space fractional quantum correction with periodic boundary condition [38] i…”

“…(−∆) β N(x, t) can be defined in the same way. The global existence and uniqueness of the solution of the system (3)-( 4) have been shown in [38]. When H = 0, the system (3)-( 4) reduces to the classical Zakharov system which has been studied extensively in [1][2][3][4][5][6][7][8][9].…”

“…When H 0, α = β = 2, the system (3)-( 4) reduces to the quantum Zakharov system (1)- (2). In fact, it is easy to show that the system (3)-( 6) satisfies the mass and energy conserved laws [38,39] d dt…”