Abstract
We prove that the uniqueness results obtained in [26] for the Benjamin equation, cannot be extended for any pair of non-vanishing solutions. On the other hand, we study uniqueness results of solutions of the Benjamin equation. With this purpose, we showed that for any solutions u and v defined in R×[0,T], if there exists an open set I⊂R such that u(⋅,0) and v(⋅,0) agree in I, ∂tu(⋅,0) and ∂tv(⋅,0) agree in I, then u≡v. A better version of this uniqueness result is also established. To finish, this type of uniqueness results were also proved for the nonlocal perturbation of the Benjamin-Ono equation (npBO) and for the regularized Benjamin-Ono equation (rBO).
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