Asymptotic Analysis· 2026Q1
On the Subcritical Fractional Modified Korteweg–de Vries Equation of Order α∈(0,1)∪(1,32]
- 0citations
- Q1SCImago
- 2026year
Short summary
This paper proves the global-in-time existence of small solutions to the Cauchy problem for a subcritical fractional modified Korteweg–de Vries (mKdV) equation with order α∈(0,1)∪(1,32] and a fractional power term ∂x(u^3).
AI-generated from the title and abstract; the full text is not read.
Key points
- Proves global-in-time existence of small solutions for a subcritical fractional mKdV equation.
- The equation involves fractional derivatives of order α∈(0,1)∪(1,32] and a nonlinear term ∂x(u^3).
- Assumes small initial data with analytic extensions in a sector and a strip.
- Derives the large-time asymptotic behavior of the solutions.
AI-generated from the title and abstract; the full text is not read.
Abstract
We study the global in time existence of small solutions to the Cauchy problem for the subcritical fractional modified Korteweg–de Vries equation { ∂ t u + 1 α | ∂ x | α − 1 ∂ x u = t ν ∂ x ( u 3 ) , t > 0 , x ∈ R , u ( 0 , x ) = u 0 ( x ) , x ∈ R , where α ∈ ( 0 , 1 ) ∪ ( 1 , 3 2 ] , 0 < ν < 1 24 . We remark that the condition ν > 0 implies that equation is subcritical in the sense of the large-time asymptotic behavior of solutions. We assume that the initial data are small and admit an analytic extension on the sector and a strip. Then we find the large time asymptotics of solutions.
The authors' abstract, as published at the source. Asymptotic Analysis, 2026 · DOI ↗
Continue with a free account
Ask the paper: 3 free questions a day about this paper; save it, get its citation, new summaries every day for your field. Takeaways are Premium.
Continue free on the webSign in with Google or Apple; no card needed. You come back to this paper.
On your phone:
Field: Mathematical Physics
Mathematical PhysicsMathematics