Bright and dark solitons on the surface of finite-depth fluid below the modulation instability threshold

Abstract

Bright and dark solitons are usually considered from the perspective of modulation instability of the carrier wave train: bright solitons are observed when the carrier wave is unstable with respect to long-wave modulations, while dark solitons are observed when the carrier wave is modulationally stable. For the slowly modulated wave trains with narrow bandwidth on the surface of ideal finite-depth fluid, the corresponding modulation instability threshold is known to lie at kh≈1.363, k being the carrier wave number and h the undisturbed fluid depth. In this case, bright solitons are known to exist above the modulation instability threshold (kh≳1.363), while dark solitons are known to exist below this threshold (kh<1.363). We demonstrate for the first time that besides these classical results bright solitons can also be observed along with dark solitons in a certain water depth range around kh≈1.2 that lies below the modulation instability threshold. We provide initial conditions at which these new bright solitons can be generated in water wave tank experiments.