[For the entire collection see Zbl 0665.00007.]
Solutions to the dissipatively perturbed Korteweg-de Vries equation \[ (1)\quad u_ t+uu_ x-\eta (u+u_{xx})+u_{xxx}=0 \] with different values of the perturbation parameter \(\eta\) are studied. For small \(\eta\), an evolution equation for an amplitude of a conoidal-wave solution with the zero value of the “mass” \(M=\int^{+\infty}_{- \infty}u(x)dx\) is derived with the help of the perturbation theory. Next, numerical simulation is developed. The numerical results demonstrate that a wave field with \(M=0\) may be regarded as a superposition of KdV-like solitons. However, collisions of two “solitons” result sometimes in their merging into one solitary pulse. The numerically observed evolution of the “soliton gas” seems, as a whole, chaotic at small \(\eta\). At sufficiently large \(\eta\) the numerical results are altogether different: After a transient period during which conoidal-like periodic arrays of pulses are observed, a stationary sawtooth-like shock wave sets in. The shock has an oscillatory structure, so that it may be regarded as a bound state of a large number of pulses with different amplitudes.