  We consider a population structured by a spacevariable and a phenotypical
trait, submitted to dispersion,mutations, growth and nonlocal competition. This
population is facing an {\it environmental gradient}: to survive at location
$x$, an individual must have a trait close to some optimal trait $y_{opt}(x)$.
Our main focus is to understand the effect of a {\it nonlinear} environmental
gradient. We thus consider a nonlocal parabolic equation for the distribution
of the population, with $y_{opt}(x) = \varepsilon\theta(x)$, $0<\vert
\varepsilon \vert \ll 1$. We construct steady states solutions and, when
$\theta$ is periodic, pulsating fronts. This requires the combination of
rigorous perturbation techniques based on a careful application of the implicit
function theorem in rather intricate function spaces. To deal with the
phenotypic trait variable $y$ we take advantage of a Hilbert basis of
$L^{2}(\mathbb{R})$ made of eigenfunctions of an underlying Schr\"odinger
operator, whereas to deal with the space variable $x$ we use the Fourier series
expansions. Our mathematical analysis reveals, in particular, how both the
steady states solutions and the fronts (speed and profile) are distorted by the
nonlinear environmental gradient, which are important biological insights.
