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We study the inhomogeneous solitonic modulation of a chiral condensate withinthe effective Nambu--Jona-Lasinio model when a constant external magnetic fieldis present. The self-consistent Pauli-Villars regularization scheme is adoptedto manipulate the ultraviolet divergence encountered in the thermodynamicquantities. In order to determine the chiral restoration lines efficiently, anew kind of Ginzburg-Landau expansion approach is proposed here. At zerotemperature, we find that both the upper and lower boundaries of the solitonicmodulation oscillate with the magnetic field in the $\mu$--$B$ phase diagramwhich is actually the de Hass-van Alphan (dHvA) oscillation. It is veryinteresting to find out how the tricritical Lifshitz point $(T_L,\mu_L)$evolves with the magnetic field: There are also dHvA oscillations in the$T_L$--$B$ and $\mu_L$--$B$ curves, though the tricritical temperature $T_L$increases monotonically with the magnetic field.

Solitonic modulation and Lifshitz point in an external magnetic field within Nambu--Jona-Lasinio model