Bright envelope solitons were theoretically predicted to exist for wave packets on the surface of an inviscid finite-depth fluid in a depth range where the carrier wave is modulationally stable. Initial conditions at which these solitons can be generated in a water wave tank were provided.

Reference: Phys. Lett. A 381, 1784 (2017)
https://doi.org/10.1016/j.physleta.2017.02.052
An hierarchy of generalised nonlinear Schrödinger equations was derived to describe the dynamics of the envelope of slowly modulated wave packets on different time scales in the nonlinear Klein–Gordon model with arbitrary polynomial nonlinearity. Temporal scales of higher orders were demonstrated to manifest themselves in a slow modulation of the constant amplitude of envelope solitons and lead to the formation of quasisolitons that propagate with almost constant velocity and pertain almost steady form during long time intervals.

Reference: Nonlin. Dyn. 98, 359 (2019)
https://doi.org/10.1007/s11071-019-05197-x
A high-order nonlinear Schrödinger equation in the nonlinear Klein–Gordon model was obtained for the first time in Hamiltonian form that does not violate the conservation of energy during the motion of the wave packet envelope. Changing the balance between the cubic and quintic nonlinearities in this model was demonstrated to have a significant effect on the stability of unmodulated wave packets to long-wave modulations.

Reference: Phys. Rev. E 106, 064212 (2022)
https://doi.org/10.1103/PhysRevE.106.064212
A new method of calculating sharp-crested gravity waves on the surface of inviscid fluid was developed. The most accurate estimates of the amplitude, speed, and energy of the limiting Stokes wave with a 120º corner at the crest were obtained. Irregular wave patterns with intricate surface profiles were calculated.

Reference:
Phys. Rev. Lett. 89, 164502 (2002)
https://doi.org/10.1103/PhysRevLett.89.164502

Proc. Roy. Soc. A 463, 1597 (2007)
https://doi.org/10.1098/rspa.2007.1840
Period doubling cascades and symmetry breaking bifurcations in the forced oscillations of a nonlinear Duffing oscillator were studied. Conditions of transition to dynamical chaos were obtained. Mechanisms of the formation of chaotic attractors were explained.

Reference: J. Sound Vib. 275, 351 (2004)
https://doi.org/10.1016/j.jsv.2003.06.029
A dynamical model for describing the spread of epidemics in a system of economic agents was proposed. This model takes into account the socioeconomic interplay between the process of epidemic spreading in population and the economic resource available to the infected agents. Strategies to mitigate the effect of epidemics were considered.

Reference:
Chaos Soliton Frac. 148, 111046 (2021)
https://doi.org/10.1016/j.chaos.2021.111046

Eur. Phys. J. B 94, 90 (2021)
https://doi.org/10.1140/epjb/s10051-021-00099-7