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math.AP2026
An explicit formula for the solution of the Benjamin-Ono equation and its applications
Louise Gassot, Patrick Gérard, Peter D. Miller
We summarize recent developments in the theory of the Benjamin-Ono equation, a well-known long-wave asymptotic model for internal waves in deep water, focusing on results obtained…
math.AP2026
The Benjamin-Ono Equation in the Long-Time Limit: Linearized Self-Similar Universality
Louise Gassot, Patrick Gérard, Peter D. Miller
We obtain the leading term in the solution of the Cauchy problem for the Benjamin-Ono equation in the limit with . We show that the rate of decay exceed…
math.AP2026
A proof of the soliton resolution conjecture for the Benjamin--Ono equation
Louise Gassot, Patrick Gérard, Peter D. Miller
We give a proof of the soliton resolution conjecture for the Benjamin--Ono equation, namely every solution with sufficiently regular and decaying initial data can be written as a f…