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20212026
most citedThe Benjamin-Ono equation in the zero-dispersion limit for rational initial data: generation of dispersive shock waves

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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…